Stochastic Processes: General Theory

Shastic Processes: General Theory starts with the fundamental existence theorem of Kolmogorov, together with several of its extensions to shastic 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: a unique feature of the book. Applications to higher order shastic differential equations and their special features are presented in detail. Shastic processes in a manifold and multiparameter shastic analysis are also discussed. Each of the seven chapters includes complements, exercises and extensive references: many avenues of research are suggested. The book is a completely revised and enlarged version of the author's Shastic Processes and Integration (Noordhoff, 1979). The new title reflects the content and generality of the extensive amount of new material. Audience: Suitable as a text/reference for second year graduate classes and seminars. A knowledge of real analysis, including Lebesgue integration, is a prerequisite.