Stochastic Processes: General Theory

This study starts with the fundamental existence theorem of Kolmogorov, together with several of its extensions to stochastic processes. It treats the function theoretical aspects of processes and includes an extended account of martingales and their generalizations. Various compositions of (quasi- or semi-)martingales and their integrals are given. Here the Bochner boundedness principle plays a unifying role. Applications to higher order stochastic differential equations and their special features are presented in detail. Stochastic processes in a manifold and multiparameter stochastic analysis are also discussed. Each of the seven chapters includes complements, exercises and references. The book is a revised and enlarged version of the author's "Stochastic Processes and Integration" (Noordhoff, 1979). The book should be suitable as a text/reference for second year graduate classes and seminars. A knowledge of real analysis, including Lebesgue integration, is a prerequisite.