Stochastic Processes: General Theory 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: a unique
feature of the book. 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 extensive references: many
avenues of research are suggested. The book is a completely revised
and enlarged version of the author's Stochastic 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.
General
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