Fixed point theorems in probabilistic analysis

1. Introduction. Probabilistic operator theory is that branch of probabilistic (or stochastic) analysis which is concerned with the study of operator-valued random variables (or, simply, random operators) and their properties. The development of a theory of random operators is of interest in its own right as a probabilistic generalization of (deterministic) operator theory; and just as operator theory is of fundamental importance in the study of operator equations, the development of probabilistic operator theory is required for the study of various classes of random equations.