Elements of Stochastic Calculus and Analysis

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Beschreibung

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.

This book gives a somewhat unconventional introduction to stochastic analysis. Although most of the material covered

lemma, theorem'' text. In addition, it includes several topics that are not usually treated elsewhere. For example,

mathematicians who may be familiar with many of the topics but want to broaden their understanding of them.

Über den Autor

Daniel W. Stroock is Professor Emeritus of Mathematics at MIT. Professor Stroock's research interests focus on probability theory and stochastic processes. Stroock (with S. Varadhan) was awarded the Leroy P. Steele Prize for seminal contributions to research in stochastic equations. In 2007, Stroock received an Honorary Fellowship at Swansea University, Wales, and in 2004 selected to be Foreign Member of the Polish Academy of Arts and Sciences. Professor Stroock is a Fellow of the American Academy of Arts and Sciences (1991), and a Member of the National Academy of Sciences (1995). Professor Stroock has made many contributions to pedagogical literature, among these include: An Introduction to Markov Processes" (GTM 230), "Essentials of Integration Theory for Analysis" (GTM 262), "Multidimensional Diffusion Processes" (Classics in Mathematics).

Zusammenfassung

Often written in a more essay form, the text contains many unique insights into the topic

Broadens understanding of the material for advanced grad students and research mathematicians

Includes unique and challenging exercises in each chapter

Includes supplementary material: [...]

Inhaltsverzeichnis

Preface.- 1. Kolmogorov's Equations.- 2. Itô's Approach.- 3. Brownian Stochastic Integration.- 4. Other Theories of Stochastic Integration.- 5. Addenda.- References.- Index.

Details

Erscheinungsjahr:	2018
Fachbereich:	Wahrscheinlichkeitstheorie
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Seiten:	220
Reihe:	CRM Short Courses
Inhalt:	xiv 206 S.
ISBN-13:	9783319770376
ISBN-10:	3319770373
Sprache:	Englisch
Herstellernummer:	978-3-319-77037-6
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Stroock, Daniel W.
Auflage:	2018
Hersteller:	Springer International Publishing Springer International Publishing AG CRM Short Courses
Maße:	241 x 160 x 18 mm
Von/Mit:	Daniel W. Stroock
Erscheinungsdatum:	07.05.2018
Gewicht:	0,5 kg

preigu-id: 111333084