Search for a command to run...
Previous article Next article A Limit Theorem for the Solutions of Differential Equations with Random Right-Hand SidesR. Z. Khas’minskiiR. Z. Khas’minskiihttps://doi.org/10.1137/1111038PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] R. Z. Khas'minskii, On stochastic processes defined by differential equations with a small parameter, Theory Prob. Applications, 11 (1966), 211–228, (English translation) 10.1137/1111018 LinkGoogle Scholar[2] R. L. Stratonovich, Topics in the theory of random noise. Vol. I: General theory of random processes. Nonlinear transformations of signals and noise, Revised English edition. Translated from the Russian by Richard A. Silverman, Gordon and Breach Science Publishers, New York, 1963xiii+292, Vol. II, (1967), (Translated by R. L. Silverman.) MR0158437 Google Scholar[3] R. L. Stratonovich, Masters Thesis, Conditional Markov Processes and Their Application to Optimal Control Theory, Doctoral Dissertation, Mosc. Univ., Moscow, 1965, (In Russian.) Google Scholar[4] I. A. Ibragimov, Some limit theorems for stochastic processes stationary in the strict sense, Dokl. Akad. Nauk SSSR, 125 (1959), 711–714, (In Russian.) MR0105180 0087.13302 Google Scholar[5] I. A. Ibragimov, Some limit theorems for stationary processes, Theory Prob. Applications, 7 (1962), 349–382, (English translation.) 10.1137/1107036 0119.14204 LinkGoogle Scholar[6] R. L. Dobrushin, The central limit theorem for nonstationary Markov chains I, II, Theory Prob. Applications, 1 (1956), 65–80; 329–383, (English translation.) Google Scholar[7] J. L. Doob, Stochastic processes, John Wiley & Sons Inc., New York, 1953viii+654 MR0058896 0053.26802 Google Scholar[8] V. A. Volkonskii˘ and , Yu. A. Rozanov, Some limit theorems for random functions. I, Theor. Probability Appl., 4 (1959), 178–197, (English translation.) MR0121856 0092.33502 LinkGoogle Scholar[9] A. V. Skorokhod, Studies in the theory of random processes, Translated from the Russian by Scripta Technica, Inc, Addison-Wesley Publishing Co., Inc., Reading, Mass., 1965viii+199 MR0185620 0146.37701 Google Scholar[10] Yu. V. Prokhorov, Convergence of stochastic processes and limit theorems in probability theory, Theory Prob. Applications, 1 (1956), 157–214, (English translation.) 10.1137/1101016 LinkGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Averaging of neutral stochastic partial functional differential equations involving delayed impulses25 May 2021 | Applicable Analysis, Vol. 101, No. 18 Cross Ref The averaging method for doubly perturbed distribution dependent SDEsStatistics & Probability Letters, Vol. 189 Cross Ref Stochastic analysis of a nonlinear energy harvester with fractional derivative damping11 March 2022 | Nonlinear Dynamics, Vol. 108, No. 3 Cross Ref Probabilistic analysis of drill string under uncertain conditions for flow velocity and axial compressive loadApplied Ocean Research, Vol. 122 Cross Ref The applicability of stochastic averaging method to solve the ship rolling response excited by narrow-band wavesOcean Engineering, Vol. 251 Cross Ref A mechanism for the skew of ensemble forecasts15 March 2022 | Quarterly Journal of the Royal Meteorological Society, Vol. 148, No. 744 Cross Ref Analytical prediction of delayed Hopf bifurcations in a simplified stochastic model of reed musical instruments13 January 2022 | Nonlinear Dynamics, Vol. 107, No. 4 Cross Ref Improved stochastic averaging method using Hamiltonian for parametric rolling in irregular longitudinal waves25 May 2021 | Journal of Marine Science and Technology, Vol. 27, No. 1 Cross Ref Averaging Principles for Stochastic 2D Navier–Stokes Equations16 January 2022 | Journal of Statistical Physics, Vol. 186, No. 2 Cross Ref Mixed Neutral Caputo Fractional Stochastic Evolution Equations with Infinite Delay: Existence, Uniqueness and Averaging Principle12 February 2022 | Fractal and Fractional, Vol. 6, No. 2 Cross Ref Response and reliability analysis of random time-delay controlled systems undergo wide-band random excitationsProbabilistic Engineering Mechanics, Vol. 67 Cross Ref Stochastic Hopf Bifurcation of MDOF Quasi-Integrable Hamiltonian Systems with Delayed Feedback Fractional-Order PD Controller2 September 2021 | International Journal of Structural Stability and Dynamics, Vol. 21, No. 13 Cross Ref A novel method for evaluating the averaged drift and diffusion coefficients of high DOF quasi-non-integrable Hamiltonian systems10 November 2021 | Nonlinear Dynamics, Vol. 106, No. 4 Cross Ref Periodic averaging theorems for neutral stochastic functional differential equations involving delayed impulses16 September 2020 | Stochastics, Vol. 93, No. 6 Cross Ref Amplitude-phase description of stochastic neural oscillators across the Hopf bifurcation9 July 2021 | Physical Review Research, Vol. 3, No. 3 Cross Ref Moment stability of viscoelastic system influenced by non-Gaussian colored noiseJournal of Sound and Vibration, Vol. 502 Cross Ref Stationary response of colored noise excited vibro-impact system*Chinese Physics B, Vol. 30, No. 6 Cross Ref Modeling of the quasi-periodic galloping response type under combined harmonic and random excitationComputers & Structures, Vol. 247 Cross Ref Averaging Principle for Backward Stochastic Differential EquationsDiscrete Dynamics in Nature and Society, Vol. 2021 Cross Ref Diffusion Approximation for Noise-Induced Evolution of First Integrals in Multifrequency Systems23 February 2021 | Journal of Statistical Physics, Vol. 182, No. 3 Cross Ref Quantum Behavior of a Classical Particle Subject to a Random Force1 February 2021 | Foundations of Physics, Vol. 51, No. 1 Cross Ref Stochastic averaging for estimating a ship roll in random longitudinal or oblique wavesMarine Structures, Vol. 75 Cross Ref Perturbed uncertain differential equations and perturbed reflected canonical processAIMS Mathematics, Vol. 6, No. 9 Cross Ref Homogenization for stochastic reaction-diffusion equations with singular perturbation termDiscrete & Continuous Dynamical Systems - B, Vol. 0, No. 0 Cross Ref Ghost attractors in blinking Lorenz and Hindmarsh–Rose systemsChaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 30, No. 8 Cross Ref First passage time of nonlinear diffusion processes with singular boundary behaviorJournal of Sound and Vibration, Vol. 476 Cross Ref Averaging Method for Neutral Stochastic Delay Differential Equations Driven by Fractional Brownian MotionJournal of Function Spaces, Vol. 2020 Cross Ref Scaling limits of processes with fast nonlinear mean reversionStochastic Processes and their Applications, Vol. 130, No. 4 Cross Ref Stochastic averaging for stochastic differential equations driven by fractional Brownian motion and standard Brownian motionApplied Mathematics Letters, Vol. 100 Cross Ref Nonstationary Seismic Responses of Nonlinear Structural Systems to Modulated Earthquake ExcitationsJournal of Engineering Mechanics, Vol. 145, No. 12 Cross Ref A Feynman–Kac formula approach for computing expectations and threshold crossing probabilities of non-smooth stochastic dynamical systemsPhysica D: Nonlinear Phenomena, Vol. 397 Cross Ref An efficient assessment of vulnerability of a ship to parametric roll in irregular seas using first passage statisticsProbabilistic Engineering Mechanics, Vol. 58 Cross Ref Hilbert Transform–Based Stochastic Averaging Technique for Determining the Survival Probability of Nonlinear OscillatorsJournal of Engineering Mechanics, Vol. 145, No. 10 Cross Ref Approximation properties for solutions to Itô–Doob stochastic fractional differential equations with non-Lipschitz coefficients30 June 2019 | Stochastics and Dynamics, Vol. 19, No. 04 Cross Ref Stochastic Dynamic Analysis of an Offshore Wind Turbine Structure by the Path Integration Method8 August 2019 | Energies, Vol. 12, No. 16 Cross Ref Approximate Analytical Solutions of Reliability for Controlled Single First-Integral Nonlinear Stochastic Systems5 February 2019 | Journal of Vibration and Acoustics, Vol. 141, No. 3 Cross Ref Spectral Dynamic Analysis of A Stationary Jack-Up Platform15 April 2019 | Polish Maritime Research, Vol. 26, No. 1 Cross Ref Stochastic averaging for two-time-scale stochastic partial differential equations with fractional Brownian motionNonlinear Analysis: Hybrid Systems, Vol. 31 Cross Ref Analyzing El Niño-Southern Oscillation Predictability Using Long-Short-Term-Memory Models18 February 2019 | Earth and Space Science, Vol. 6, No. 2 Cross Ref Stochastic Dynamic Security of Power System24 August 2018 Cross Ref Stochastic Bifurcation of a Strongly Non-Linear Vibro-Impact System with Coulomb Friction under Real Noise21 December 2018 | Symmetry, Vol. 11, No. 1 Cross Ref Linear or Nonlinear Modeling for ENSO Dynamics?8 November 2018 | Atmosphere, Vol. 9, No. 11 Cross Ref Estimate of the average timing for strong El Niño events using the recharge oscillator model with a multiplicative perturbationChaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 28, No. 10 Cross Ref Rupture Detection in Fatigue Crack Propagation6 August 2018 Cross Ref Averaging principles for SPDEs driven by fractional Brownian motions with random delays modulated by two-time-scale Markov switching processes10 August 2018 | Stochastics and Dynamics, Vol. 18, No. 04 Cross Ref Stochastic averaging principles for multi-valued stochastic differential equations driven by poisson point Processes30 April 2018 | Stochastic Analysis and Applications, Vol. 36, No. 4 Cross Ref Stochastic subgrid‐scale parametrization for one‐dimensional shallow‐water dynamics using stochastic mode reduction10 October 2018 | Quarterly Journal of the Royal Meteorological Society, Vol. 144, No. 715 Cross Ref Modeling the lake eutrophication stochastic ecosystem and the research of its stabilityMathematical Biosciences, Vol. 300 Cross Ref Pendulum energy converter excited by random loads3 November 2017 | ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 98, No. 3 Cross Ref Divergence instability of pipes conveying fluid with uncertain flow velocityPhysica A: Statistical Mechanics and its Applications, Vol. 491 Cross Ref Averaging principles for functional stochastic partial differential equations driven by a fractional Brownian motion modulated by two-time-scale Markovian switching processesNonlinear Analysis: Hybrid Systems, Vol. 27 Cross Ref Stochastic response of Duffing-Van der Pol vibro-impact system with viscoelastic term under wide-band excitationChaos, Solitons & Fractals, Vol. 104 Cross Ref Reduced α -stable dynamics for multiple time scale systems forced with correlated additive and multiplicative Gaussian white noiseChaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 27, No. 11 Cross Ref Strong Averaging Along Foliated Lévy Diffusions with Heavy Tails on Compact Leaves2 March 2017 | Potential Analysis, Vol. 47, No. 3 Cross Ref Stochastic averaging for a class of two-time-scale systems of stochastic partial differential equationsNonlinear Analysis, Vol. 160 Cross Ref On dynamical systems perturbed by a null-recurrent motion: The general caseStochastic Processes and their Applications, Vol. 127, No. 6 Cross Ref Stochastic averaging principle for differential equations with non-Lipschitz coefficients driven by fractional Brownian motion23 March 2017 | Stochastics and Dynamics, Vol. 17, No. 02 Cross Ref Stochastic Parameterization: Toward a New View of Weather and Climate Models31 March 2017 | Bulletin of the American Meteorological Society, Vol. 98, No. 3 Cross Ref Two-time-scales hyperbolic–parabolic equations driven by Poisson random measures: Existence, uniqueness and averaging principlesJournal of Mathematical Analysis and Applications, Vol. 447, No. 1 Cross Ref First-exit problem of MDOF strongly nonlinear oscillators under wide-band random excitations without internal resonances27 August 2016 | Acta Mechanica, Vol. 228, No. 1 Cross Ref Stability and post-critical behavior of a two-degrees of freedom aero-elastic system in a cross flowProcedia Engineering, Vol. 199 Cross Ref An improved energy envelope stochastic averaging method and its application to a nonlinear oscillator9 August 2016 | Journal of Vibration and Control, Vol. 23, No. 1 Cross Ref Stochastic responses of a vibro-impact system with additive and multiplicative colored noise excitations16 December 2014 | International Journal of Dynamics and Control, Vol. 4, No. 4 Cross Ref First-passage problem of a class of internally resonant quasi-integrable Hamiltonian system under wide-band stochastic excitationsInternational Journal of Non-Linear Mechanics, Vol. 85 Cross Ref Quasi hamilton system stochastic averaging and EEAC combined transient stability analysis method Cross Ref Effects of habitat complexity on stochastic nonlinear ecosystems20 June 2015 | International Journal of Dynamics and Control, Vol. 4, No. 3 Cross Ref Response analysis for a vibroimpact Duffing system with bilateral barriers under external and parametric Gaussian white noisesChaos, Solitons & Fractals, Vol. 87 Cross Ref Analytical and Semi-analytical Solutions of Some Fundamental Nonlinear Stochastic Differential EquationsProcedia IUTAM, Vol. 19 Cross Ref Phase Noise Reduction and Optimal Operating Conditions for a Pair of Synchronized OscillatorsIEEE Transactions on Circuits and Systems I: Regular Papers, Vol. 63, No. 1 Cross Ref Stochastic averaging for slow-fast dynamical systems with fractional Brownian motionDiscrete and Continuous Dynamical Systems - Series B, Vol. 20, No. 7 Cross Ref Analysis and control for transient responses of seismic-excited hysteretic structuresSoil Dynamics and Earthquake Engineering, Vol. 73 Cross Ref Stochastic Averaging of Dynamical Systems with Multiple Time Scales Forced with $\alpha$-Stable NoiseW. F. Thompson, R. A. Kuske, and A. H. Monahan27 October 2015 | Multiscale Modeling & Simulation, Vol. 13, No. 4AbstractPDF (655 KB)Technical Background26 July 2015 Cross Ref Stochastic Analysis of Nonlinear Systems11 October 2015 Cross Ref Stochastic stability of SDOF linear viscoelastic system under wideband noise excitationProbabilistic Engineering Mechanics, Vol. 39 Cross Ref 1/3 SUBHARMONIC RESPONSE OF DUFFING OSCILLATOR UNDER PERIODIC AND RANDOM EXCITATIONS30 December 2014 | Вестник Донского государственного технического университета, Vol. 14, No. 4 Cross Ref Moment Lyapunov exponents of the Parametrical Hill's equation under the excitation of two correlated wideband noisesStructural Engineering and Mechanics, Vol. 52, No. 3 Cross Ref An Averaging Principle for Multivalued Stochastic Differential Equations21 October 2014 | Stochastic Analysis and Applications, Vol. 32, No. 6 Cross Ref Higher-order stochastic averaging to study stability of a fractional viscoelastic columnJournal of Sound and Vibration, Vol. 333, No. 23 Cross Ref First-passage failure of preisach hysteretic systemsActa Mechanica Solida Sinica, Vol. 27, No. 5 Cross Ref Constructing transient response probability density of non-linear system through complex fractional momentsInternational Journal of Non-Linear Mechanics, Vol. 65 Cross Ref Finite element solution of Fokker–Planck equation of nonlinear oscillators subjected to colored non-Gaussian noiseProbabilistic Engineering Mechanics, Vol. 38 Cross Ref Nonstationary response of nonlinear oscillators with optimal bounded control and broad-band noisesProbabilistic Engineering Mechanics, Vol. 38 Cross Ref A weak energy–momentum method for stochastic instability induced by dissipation and random excitationsProbabilistic Engineering Mechanics, Vol. 37 Cross Ref Response analysis of Van der Pol oscillator subjected to harmonic and random excitationsProbabilistic Engineering Mechanics, Vol. 37 Cross Ref Stochastic Responses of Duffing-Van Der Pol Vibro-Impact Oscillator with Colored Noise7 July 2014 Cross Ref Stochastic Averaging for Quasi-Integrable Hamiltonian Systems With Variable Mass10 December 2013 | Journal of Applied Mechanics, Vol. 81, No. 5 Cross Ref Stochastic averaging of quasi-integrable and non-resonant Hamiltonian systems under combined Gaussian and Poisson white noise excitations10 January 2014 | Nonlinear Dynamics, Vol. 76, No. 2 Cross Ref Stochastic Averaging of Quasi-Integrable and Resonant Hamiltonian Systems Under Combined Gaussian and Poisson White Noise Excitations23 September 2013 | Journal of Applied Mechanics, Vol. 81, No. 4 Cross Ref Stochastic averaging principle for dynamical systems with fractional Brownian motionDiscrete and Continuous Dynamical Systems - Series B, Vol. 19, No. 4 Cross Ref Stochastic forcing of north tropical Atlantic sea surface temperatures by the North Atlantic Oscillation18 March 2014 | Geophysical Research Letters, Vol. 41, No. 6 Cross Ref Stochastic stability of a fractional viscoelastic column under bounded noise excitationJournal of Sound and Vibration, Vol. 333, No. 6 Cross Ref Stochastic averaging of quasi-partially integrable Hamiltonian systems under combined Gaussian and Poisson white noise excitationsPhysica A: Statistical Mechanics and its Applications, Vol. 398 Cross Ref A partial history of the early development of continuous-time nonlinear stochastic systems theoryAutomatica, Vol. 50, No. 2 Cross Ref Nonconventional limit theorems in averagingAnnales de l'Institut Henri Poincaré, Probabilités et Statistiques, Vol. 50, No. 1 Cross Ref FE based solution of FPK equations for nonlinear oscillators driven by colored Gaussian noise13 January 2014 Cross Ref Homogenization Driven by a Fractional Brownian Motion: The Shear Layer CaseTomasz Komorowski, Alexei Novikov, and Lenya Ryzhik3 April 2014 | Multiscale Modeling & Simulation, Vol. 12, No. 2AbstractPDF (287 KB)Random Vibration of a Nonlinear Autoparametric System14 December 2013 Cross Ref Stochastic Analysis of Nonlinear Systems24 September 2014 Cross Ref A limit theorem for the solutions of slow-fast systems with fractional Brownian motionTheoretical and Applied Mechanics Letters, Vol. 4, No. 1 Cross Ref Stochastic approach to diffusion inside the chaotic layer of a resonance13 January 2014 | Physical Review E, Vol. 89, No. 1 Cross Ref An Averaging Principle for Stochastic Differential Delay Equations with Fractional Brownian MotionAbstract and Applied Analysis, Vol. 2014 Cross Ref Asymptotic stability with probability one of MDOF nonlinear oscillators with fractional derivative damping3 October 2013 | Science China Physics, Mechanics and Astronomy, Vol. 56, No. 11 Cross Ref Stabilization of Quasi Integrable Hamiltonian Systems With Fractional Derivative Damping by Using Fractional Optimal ControlIEEE Transactions on Automatic Control, Vol. 58, No. 11 Cross Ref Stochastic responses of Duffing—Van der Pol vibro-impact system under additive colored noise excitation15 November 2013 | Chinese Physics B, Vol. 22, No. 11 Cross Ref Stochastic dynamics on slow manifolds27 June 2013 | Journal of Physics A: Mathematical and Theoretical, Vol. 46, No. 29 Cross Ref First-passage problem of strongly nonlinear stochastic oscillators with external and internal resonancesEuropean Journal of Mechanics - A/Solids, Vol. 39 Cross Ref Stochastic stability of quasi non-integrable Hamiltonian systems under parametric excitations of Gaussian and Poisson white noisesProbabilistic Engineering Mechanics, Vol. 32 Cross Ref Separation of time-scales and model reduction for stochastic reaction networksThe Annals of Applied Probability, Vol. 23, No. 2 Cross Ref Stochastic analysis of dynamical system with double-well potential13 March 2013 | International Journal of Dynamics and Control, Vol. 1, No. 1 Cross Ref Random perturbations effects on the stability of Tension Leg Platforms in offshore engineering and of other large structuresApplied Mathematical Modelling, Vol. 37, No. 5 Cross Ref Balanced Averaging of Bilinear Systems with Applications to Stochastic ControlCarsten Hartmann, Boris Schäfer-Bung, and Anastasia Thöns-Zueva4 June 2013 | SIAM Journal on Control and Optimization, Vol. 51, No. 3AbstractPDF (556 KB)Stochastic Regular Grazing BifurcationsD. J. W. Simpson, S. J. Hogan, and R. Kuske4 April 2013 | SIAM Journal on Applied Dynamical Systems, Vol. 12, No. 2AbstractPDF (1056 KB)Dynamics of Stochastically Blinking Systems. Part I: Finite Time PropertiesMartin Hasler, Vladimir Belykh, and Igor Belykh20 June 2013 | SIAM Journal on Applied Dynamical Systems, Vol. 12, No. 2AbstractPDF (2536 KB)Dynamics of Stochastically Blinking Systems. Part II: Asymptotic PropertiesMartin Hasler, Vladimir Belykh, and Igor Belykh20 June 2013 | SIAM Journal on Applied Dynamical Systems, Vol. 12, No. 2AbstractPDF (1427 KB)Localization and Metastability19 June 2013 Cross Ref Stochastic Averaging of Roll-Pitch and Roll-Heave Motion in Random SeasProcedia IUTAM, Vol. 6 Cross Ref Stochastic stability of the harmonically and randomly excited Duffing oscillator with damping modeled by a fractional derivative6 September 2012 | Science China Physics, Mechanics and Astronomy, Vol. 55, No. 12 Cross Ref Almost sure asymptotic stability of rotor systems subjected to stochastical axial loadsMechanism and Machine Theory, Vol. 58 Cross Ref Particle filtering in high-dimensional chaotic systemsChaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 22, No. 4 Cross Ref Stochastic fractional optimal control of quasi-integrable Hamiltonian system with fractional derivative damping2 August 2012 | Nonlinear Dynamics, Vol. 70, No. 2 Cross Ref First-passage failure of Duhem hysteretic systems14 June 2012 | Acta Mechanica, Vol. 223, No. 9 Cross Ref Stochastic Hopf bifurcation of quasi-integrable Hamiltonian systems with multi-time-delayed feedback control and wide-band noise excitations13 January 2012 | Nonlinear Dynamics, Vol. 69, No. 3 Cross Ref Numerical schemes for stability in probability of perturbed dynamical systems17 August 2012 | International Applied Mechanics, Vol. 48, No. 4 Cross Ref Alternative interpretations of power-law distributions found in natureChaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 22, No. 2 Cross Ref STOCHASTIC HOPF BIFURCATION OF QUASI-INTEGRABLE HAMILTONIAN SYSTEMS WITH FRACTIONAL DERIVATIVE DAMPING23 May 2012 | International Journal of Bifurcation and Chaos, Vol. 22, No. 04 Cross Ref Stochastic stability of viscoelastic system under non-Gaussian colored noise excitation13 February 2012 | Science China Physics, Mechanics and Astronomy, Vol. 55, No. 3 Cross Ref Nonstationary seismic responses of structure with nonlinear stiffness to modulated April | Earthquake Engineering & Structural Dynamics, Vol. 41, No. 2 Cross Ref to Averaging Cross Ref Stochastic Averaging for Asymptotic Stability Cross Ref Numerical solutions of Fokker–Planck equation of nonlinear systems subjected to random and harmonic excitationsProbabilistic Engineering Mechanics, Vol. 27, No. 1 Cross Ref Stochastic Stability of Oscillator by a Gaussian in Engineering, Vol. 2012 Cross Ref solution of Fokker–Planck bifurcation and of nonlinear January 2012 | International Journal of in Engineering and Applied Mathematics, Vol. 3, No. Cross Ref H. Cross Ref Stochastic Stability of Der Pol System with Delayed Feedback September | Applied Mechanics and Vol. Cross Ref March 2012 Cross Ref First-passage failure of MDOF nonlinear June | Science China Vol. No. 8 Cross Ref An averaging principle for stochastic dynamical systems with Lévy D: Nonlinear Phenomena, Vol. No. Cross Ref Random of viscoelastic system under broad-band excitationsInternational Journal of Non-Linear Mechanics, Vol. 46, No. 5 Cross Ref of nonlinear stochastic dynamical systems under Lévy by a April | Journal of Physics A: Mathematical and Theoretical, Vol. No. 18 Cross Ref A Stochastic for A. and August | SIAM Journal on Applied Mathematics, Vol. No. 4AbstractPDF Control for Stationary Response of Strongly Nonlinear under Combined and Noise in Engineering, Vol. Cross Ref Stability of Stochastic December Cross Ref A stochastic complex model with random June | Nonlinear Dynamics, Vol. No. 3 Cross Ref limits for in a random and Vol. 3, No. 4 Cross Ref Stochastically forced in a March | of the Royal A: Physical and Engineering Vol. No. Cross Ref Effects of on in and of and Vol. 9, No. 8 Cross Ref reduction in nonlinear January | Vol. 23, No. 2 Cross Ref Stochastic Averaging on the Infinite for and March | SIAM Journal on Control and Optimization, Vol. 48, No. and in a Random Cross Ref A linear stochastic model of tropical sea surface temperatures to El Niño Cross Ref Path of Fokker–Planck Response and Bifurcation of Nonlinear November | Journal of and Nonlinear Dynamics, Vol. No. 1 Cross Ref Stochastic averaging on time for a class of nonlinear systems with stochastic perturbation Cross Ref Asymptotic Lyapunov stability with probability one of quasi linear systems to multi-time-delayed feedback control and wide-band parametric random December | of Applied Mechanics, Vol. No. 11 Cross Ref Asymptotic Lyapunov stability with probability one of Duffing oscillator to feedback control and bounded noise December | Acta Mechanica, Vol. No. Cross Ref Dynamic in a subjected to stochastic Engineering Mechanics, Vol. No. 4 Cross Ref of the noise on the diffusion in a stochastic July | Physical Review E, Vol. No. 1 Cross Ref Climate with Linear March | Journal of Vol. 22, No. 5 Cross Ref First Dynamics of Stochastic with Optimal Control Cross Ref Numerical of Stochastic Differential Equations in Climate Cross Ref Stochastic averaging of Hamiltonian Journal of Non-Linear Mechanics, Vol. No. 1 Cross Ref Stochastic averaging method for estimating of excited March | Acta Mechanica Sinica, Vol. No. 5 Cross Ref Stochastic Averaging of Strongly Nonlinear Under Combined and Noise August | Journal of Vibration and Acoustics, Vol. 130, No. 5 Cross Ref On systems with stochastic diffusion Lévy May | Transactions of the Royal A: Physical and Engineering Vol. No. Cross Ref First-passage failure of strongly nonlinear oscillators under combined harmonic and noise September | of Applied Mechanics, Vol. No. 7 Cross Ref of a by additive stochastic averaging Journal of Mathematics, Vol. No. 6 Cross Ref Stability of SDOF Linear System Under the of February | Journal of Applied Mechanics, Vol. No. 2 Cross Ref of a Heavy Particle in a of and April | Multiscale Modeling & Simulation, Vol. No. slow and fast in stochastic dynamical systemsPhysica A: Statistical Mechanics and its Applications, Vol. No. 1 Cross Ref Stochastic Averaging and Optimal May | Journal of Vibration and Acoustics, Vol. No. 6 Cross Ref OF A RANDOM January 2012 | and Noise Letters, Vol. No. 04 Cross Ref The study on stationary solution of a complex dynamical A: Statistical Mechanics and its Applications, Vol. No. 2 Cross Ref diffusion controlled reaction of driven by broad-band October | The Physical Journal B, Vol. No. 3 Cross Ref Stochastic averaging of MDOF quasi integrable Hamiltonian systems under wide-band random excitationJournal of Sound and Vibration, Vol. No. Cross Ref of and Ocean With and Stochastic Ocean September | Applied Mechanics Vol. No. 5 Cross Ref Asymptotic for and June | Vol. 20, No. 7 Cross Ref Moment Lyapunov exponents of a system under combined harmonic and noise of Sound and Vibration, Vol. No. Cross Ref Topics in Stochastic D: Nonlinear Phenomena, Vol. No. Cross Ref On
Published in: Theory of Probability and Its Applications
Volume 11, Issue 3, pp. 390-406
DOI: 10.1137/1111038