Stochastic Processes: General Theory (Hardcover)
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|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 authors 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. *Author: Rao, M. M./ Rao, Malempati M. *Series Title: Environmental Science and Technology Library *Series Number: 342 *Binding Type: Hardcover *Number of Pages: 660 *Publication Date: 1995/10/31 *Language: English *Dimensions: 7.00 x 9.99 x 1.43 inches|
From the Publisher:
A text/reference for advanced graduate courses and seminars, being a revised and expanded version of the author's Stochastic Processes and Integration (Noordhoff, 1979). The first five chapters are devoted to the general theory of processes, and the final two are largely new. A major difference of this version is the inclusion of a generalized version of Bochner's boundedness principle which enables a novel unification of all the currently used stochastic integrals. This plays a key role in Chapter 6, where both linear and nonlinear higher order stochastic differential equations are presented as applications of this idea. Chapter 7 continues the same general theme, but for processes taking values in smooth manifolds or for multiparameters. Assumes a knowledge of real analysis including Lebesgue integration. Annotation c. by Book News, Inc., Portland, Or.