Elements of Stochastic Calculus and Analysis

Stroock, Daniel W.

ISBN 10: 3319770373 / ISBN 13: 9783319770376

Verlag: Springer, 2018

Beschreibung

Bestandsnummer des Verkäufers 31311705-n

Bibliografische Details

Titel: Elements of Stochastic Calculus and Analysis

Verlag: Springer

Erscheinungsdatum: 2018

Einband: Hardcover

Zustand: New

Über diesen Titel

Inhaltsangabe:

<DIV>THIS BOOK GIVES A SOMEWHAT UNCONVENTIONAL INTRODUCTION TO&NBSP;&NBSP;STOCHASTIC ANALYSIS.&NBSP; ALTHOUGH MOST OF THE MATERIAL COVERED</DIV><DIV>HERE HAS APPEARED IN OTHER PLACES, THIS BOOK ATTEMPTS TO EXPLAIN THE&NBSP;CORE IDEAS ON WHICH THAT MATERIAL IS BASED.&NBSP; AS A CONSEQUENCE, THE&NBSP;PRESENTATION IS MORE AN EXTENDED MATHEMATICAL ESSAY THAN A ``DEFINITION,</DIV><DIV>LEMMA, THEOREM'' TEXT.&NBSP; IN ADDITION, IT INCLUDES&NBSP;SEVERAL TOPICS THAT ARE NOT USUALLY TREATED ELSEWHERE.&NBSP; FOR EXAMPLE,</DIV><DIV>WIENER'S THEORY OF HOMOGENEOUS CHAOS IS DISCUSSED, STRATOVICH INTEGRATION&NBSP;IS GIVEN A NOVEL DEVELOPMENT AND APPLIED TO DERIVE WONG AND ZAKAI'S&NBSP;APPROXIMATION THEOREM, AND EXAMPLES ARE GIVEN OF THE APPLICATION OF</DIV><DIV>MALLIAVIN'S CALCULUS TO PARTIAL DIFFERENTIAL EQUATIONS.&NBSP; EACH CHAPTER&NBSP;CONCLUDES WITH SEVERAL EXERCISES, SOME OF WHICH ARE QUITE CHALLENGING.&NBSP; THE&NBSP;BOOK IS INTENDED FOR USE BY ADVANCED GRADUATE STUDENTS AND RESEARCH</DIV><DIV>MATHEMATICIANS WHO MAY BE FAMILIAR WITH MANY OF THE TOPICS BUT WANT TO&NBSP;BROADEN THEIR UNDERSTANDING OF THEM.</DIV>

Reseña del editor:

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.