Elements of Stochastic Calculus and Analysis. 1st ed. 2018

種類:

電子ブック

責任表示:

by Daniel W. Stroock

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2018

著者名:

• Stroock, Daniel W.
• SpringerLink (Online service)

シリーズ名:

CRM Short Courses ;

ISBN:

9783319770383 [3319770381]    

注記:

Preface -- 1. Kolmogorov's Equations -- 2. Itô's Approach -- 3. Brownian Stochastic Integration -- 4. Other Theories of Stochastic Integration -- 5. Addenda -- References -- Index. .
This book gives a somewhat unconventional introduction to stochastic analysis. Although most of the material covered here has appeared in other places, this book attempts to explain the core ideas on which that material is based. As a consequence, the presentation is more an extended mathematical essay than a ``definition, lemma, theorem'' text. In addition, it includes several topics that are not usually treated elsewhere. For example, Wiener's theory of homogeneous chaos is discussed, Stratovich integration is given a novel development and applied to derive Wong and Zakai's approximation theorem, and examples are given of the application of Malliavin's calculus to partial differential equations. Each chapter concludes with several exercises, some of which are quite challenging. The book is intended for use by advanced graduate students and research mathematicians who may be familiar with many of the topics but want to broaden their understanding of them.

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