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Universitext

Stochastic Partial Differential Equations

Authors: Lototsky, Sergey V., Rozovsky, Boris L.

  • Covers material for about 40 hours of lectures for everybody working in the area of stochastic analysis, from beginning graduate students to experts in the field
  • Presents exercise material to fill potential exams and homework assignments, and gives hints that can lead to solutions.
  • Provides all the necessary background from functional analysis and the theory of PDEs
  • Gives all necessary tools to understand the proofs of existing theorems about SPDEs (from other sources) and  even to formulate and prove a few new ones
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Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-3-319-58647-2
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $89.99
price for USA
  • ISBN 978-3-319-58645-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

Taking readers with a basic knowledge of probability and real analysis to the frontiers of a very active research discipline, this textbook provides all the necessary background from functional analysis and the theory of PDEs. It covers the main types of equations (elliptic, hyperbolic and parabolic) and discusses different types of random forcing. The objective is to give the reader the necessary tools to understand the proofs of existing theorems about SPDEs (from other sources) and perhaps even to formulate and prove a few new ones. Most of the material could be covered in about 40 hours of lectures, as long as not too much time is spent on the general discussion of stochastic analysis in infinite dimensions.

 As the subject of SPDEs is currently making the transition from the research level to that of a graduate or even undergraduate course, the book attempts to present enough exercise material to fill potential exams and homework assignments. Exercises appear throughout and are usually directly connected to the material discussed at a particular place in the text. The questions usually ask to verify something, so that the reader already knows the answer and, if pressed for time, can move on. Accordingly, no solutions are provided, but there are often hints on how to proceed.

The book will be of interest to everybody working in the area of stochastic analysis, from beginning graduate students to experts in the field.

About the authors

Sergey Lototsky earned a Master’s degree in Physics in 1992 from the Moscow Institute of Physics and Technology, followed by a PhD in Applied Mathematics in 1996 from the University of Southern California. After a year-long post-doc at the Institute for Mathematics and its Applications and a three-year term as a Moore Instructor at MIT, he returned to the department of Mathematics at USC as a faculty member in 2000. He specializes in stochastic analysis, with emphasis on stochastic differential equations. He has supervised more than 10 PhD students and has held visiting positions at the Mittag-Leffler Institute in Sweden and at several universities in Israel and Italy.

Boris Rozovsky earned a Master’s degree in Probability and Statistics, followed by a Ph.D. in Physical and Mathematical Sciences, both from the Moscow State (Lomonosov) University. He was Professor of Mathematics and Director of the Center for Applied Mathematical Sciences at the University of Southern California.  Currently, he is the Ford Foundation Professor of Applied Mathematics at Brown University.

Table of contents (6 chapters)

  • Introduction

    Lototsky, Sergey V. (et al.)

    Pages 1-23

  • Basic Ideas

    Lototsky, Sergey V. (et al.)

    Pages 25-73

  • Stochastic Analysis in Infinite Dimensions

    Lototsky, Sergey V. (et al.)

    Pages 75-142

  • Linear Equations: Square-Integrable Solutions

    Lototsky, Sergey V. (et al.)

    Pages 143-232

  • The Polynomial Chaos Method

    Lototsky, Sergey V. (et al.)

    Pages 233-380

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-3-319-58647-2
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $89.99
price for USA
  • ISBN 978-3-319-58645-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Stochastic Partial Differential Equations
Authors
Series Title
Universitext
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-58647-2
DOI
10.1007/978-3-319-58647-2
Softcover ISBN
978-3-319-58645-8
Series ISSN
0172-5939
Edition Number
1
Number of Pages
XIV, 508
Number of Illustrations and Tables
1 b/w illustrations
Topics