Dependence with complete connections and its applications

1 FUNDAMENTAL NOTIONS 1.1 The concept of a random system with complete connections 1.2 Examples 1.3 Classification problems 2 ERGODICITY 2.1 Implications of ergodicity 2.2 The homogeneous case 2.3 The non-homogeneous case 2.4 An application to the associated Markov chain 3 THE ASSOCIATED MARKOV CHAIN 3.1 Associated operators 3.2 Compact Markov chains 3.3 Continuous Markov chains 3.4 Applications to ergodicity 4 ASYMPTOTIC BEHAVIOUR 4.1 Limit theorems for the infinite order chain 4.2 Limit theorems for the associated Markov chain 5 SOME SPECIAL SYSTEMS 5.1 OM chains 5.2 The continued fraction expansion 5.3 Piecewise monotonic transformations 5.4 f-expansions 5.5 Strict-sense infinite-order chains Appendix 1 Spaces, measures, and functions Appendix 2 Notions of functional analysis Appendix 3 Mixing and Markovian dependence.