Elements of Stochastic Calculus and Analysis
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※上記表示の販売価格は割引適用後の価格です 出版済み 3週間でお届けいたします。 1st ed. 2018 Series: CRM Short Courses Author: Stroock, Daniel W. Publisher: Springer ISBN: 9783319770376 Cover: HARDCOVER Date: 2018年05月 DESCRIPTION This book gives a somewhat unconventional introduction to stochastic analysis. Although most of the material coveredhere 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 ofMalliavin'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 researchmathematicians who may be familiar with many of the topics but want to broaden their understanding of them. Table of Contents Preface.- 1. Kolmogorov's Equations.- 2. Ito's Approach.- 3. Brownian Stochastic Integration.- 4. Other Theories of Stochastic Integration.- 5. Addenda.- References.- Index. TABLE OF CONTENTS This book gives a somewhat unconventional introduction to stochastic analysis. Although most of the material coveredhere 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 ofMalliavin'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 researchmathematicians who may be familiar with many of the topics but want to broaden their understanding of them.
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