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Stochastic Processes: General Theory

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概要 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 as...pects 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.続きを見る
目次 I: Introduction and foundations
II: Conditioning and martingales
III: Stochastic function theory
IV: Refinements in martingale analysis
V: Martingale decompositions and integration
VI: Stochastic integrals and differential systems
VII: Stochastic analysis on differential structures
Notation index
Author index.
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登録日 2020.06.27
更新日 2020.06.28