Table of contents

  1. Front Matter
    Pages I-XVI
  2. Stochastic Differential Equations in Infinite Dimensions

    1. Front Matter
      Pages 1-1
    2. Leszek Gawarecki, Vidyadhar Mandrekar
      Pages 3-16
    3. Leszek Gawarecki, Vidyadhar Mandrekar
      Pages 17-72
    4. Leszek Gawarecki, Vidyadhar Mandrekar
      Pages 73-149
    5. Leszek Gawarecki, Vidyadhar Mandrekar
      Pages 151-184
    6. Leszek Gawarecki, Vidyadhar Mandrekar
      Pages 185-200
  3. Stability, Boundedness, and Invariant Measures

    1. Front Matter
      Pages 201-201
    2. Leszek Gawarecki, Vidyadhar Mandrekar
      Pages 203-231
    3. Leszek Gawarecki, Vidyadhar Mandrekar
      Pages 233-283
  4. Back Matter
    Pages 285-291

About this book

Introduction

The systematic study of existence, uniqueness, and properties of solutions to stochastic differential equations in infinite dimensions arising from practical problems characterizes this volume that is intended for graduate students and for pure and applied mathematicians, physicists, engineers, professionals working with mathematical models of finance. Major methods include compactness, coercivity, monotonicity, in a variety of set-ups. The authors emphasize the fundamental work of Gikhman and Skorokhod on the existence and uniqueness of solutions to stochastic differential equations and present its extension to infinite dimension. They also generalize the work of Khasminskii on stability and stationary distributions of solutions. New results, applications, and examples of stochastic partial differential equations are included. This clear and detailed presentation gives the basics of the infinite dimensional version of the classic books of Gikhman and Skorokhod and of Khasminskii in one concise volume that covers the main topics in infinite dimensional stochastic PDE’s. By appropriate selection of material, the volume can be adapted for a 1- or 2-semester course, and can prepare the reader for research in this rapidly expanding area.

Keywords

35-XX, 60-XX infinite dimensions stochastic differential equations

Authors and affiliations

  • Leszek Gawarecki
    • 1
  • Vidyadhar Mandrekar
    • 2
  1. 1., Dept. Science and MathematicsKettering UniversityFlintUSA
  2. 2., Dept. Statistics and ProbabilityMichigan State UniversityEast LansingUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-16194-0
  • Copyright Information Springer-Verlag Berlin Heidelberg 2011
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-16193-3
  • Online ISBN 978-3-642-16194-0
  • Series Print ISSN 1431-7028
  • About this book