Stochastic Processes: General Theory

Malempati M Rao

ISBN 10: 0792337255 / ISBN 13: 9780792337256

Editore: Springer Us Okt 1995, 1995

Neuware - 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. Codice articolo 9780792337256

Riassunto:

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.

Contenuti: Preface. 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. Bibliography. Notation index. Author index. Subject index.

Dati bibliografici

Titolo: Stochastic Processes: General Theory
Casa editrice: Springer Us Okt 1995
Data di pubblicazione: 1995
Legatura: Buch
Condizione: Neu