Overview

Preface In the axioms of probability theory proposed by Kolmogorov the basic ""probabilistic"" object is the concept of a probability model or probability space. This is a triple (n, F, P), where n is the space of elementary events or outcomes, F is a a-algebra of subsets of n announced by the events and P is a probability measure or a probability on the measure space (n, F). This generally accepted system of axioms of probability theory proved to be so successful that, apart from its simplicity, it enabled one to embrace the classical branches of probability theory and, at the same time, it paved the way for the development of new chapters in it, in particular, the theory of random (or stochastic) processes. In the theory of random processes, various classes of processes have been studied in depth. Theories of processes with independent increments, Markov processes, stationary processes, among others, have been constructed. In the formation and development of the theory of random processes, a significant event was the realization that the construction of a ""general theory of ran­ dom processes"" requires the introduction of a flow of a-algebras (a filtration) F = (Ftk::o supplementing the triple (n, F, P), where F is interpreted as t the collection of events from F observable up to time t.

Full Product Details

Author:   Yurij V. Prokhorov ,  P.B. Slater ,  S.V. Anulova ,  Albert N. Shiryaev
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   Softcover reprint of hardcover 1st ed. 1998
Volume:   45
Dimensions:   Width: 15.50cm , Height: 1.40cm , Length: 23.50cm
Weight:   0.454kg
ISBN:  

9783642081224

ISBN 10:   3642081223
Pages:   256
Publication Date:   01 December 2010
Audience:   Professional and scholarly ,  Professional and scholarly ,  Professional & Vocational ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

1. Introduction to Stochastic Calculus.- 2. Stochastic Differential and Evolution Equations.- 3. Stochastic Calculus on Filtered Probability Spaces.- 4. Martingales and Limit Theorems for Stochastic Processes.- Author Index.

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