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Stochastic Differential Equations in Infinite Dimensions

with Applications to Stochastic Partial Differential Equations

  • Textbook
  • © 2011

Overview

Authors:
  1. Leszek Gawarecki

    1. , Dept. Science and Mathematics, Kettering University, Flint, USA

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    You can also search for this author in PubMed   Google Scholar

  2. Vidyadhar Mandrekar

    1. , Dept. Statistics and Probability, Michigan State University, East Lansing, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Most comprehensive coverage of the modern techniques used for solving problems in infinite dimensional stochastic differential equations
  • Presents major methods, including compactness, coercivity, monotonicity, in different set-ups
  • Provides a broad range of new results and applications
  • Includes supplementary material: sn.pub/extras

Part of the book series: Probability and Its Applications (PIA)

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Table of contents (7 chapters)

  1. Front Matter

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

    1. Front Matter

      Pages 1-1
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    2. Partial Differential Equations as Equations in Infinite Dimensions

      • Leszek Gawarecki, Vidyadhar Mandrekar
      Pages 3-16

    3. Stochastic Calculus

      • Leszek Gawarecki, Vidyadhar Mandrekar
      Pages 17-72

    4. Stochastic Differential Equations

      • Leszek Gawarecki, Vidyadhar Mandrekar
      Pages 73-149

    5. Solutions by Variational Method

      • Leszek Gawarecki, Vidyadhar Mandrekar
      Pages 151-184

    6. Stochastic Differential Equations with Discontinuous Drift

      • Leszek Gawarecki, Vidyadhar Mandrekar
      Pages 185-200

  3. Stability, Boundedness, and Invariant Measures

    1. Front Matter

      Pages 201-201
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    2. Stability Theory for Strong and Mild Solutions

      • Leszek Gawarecki, Vidyadhar Mandrekar
      Pages 203-231

    3. Ultimate Boundedness and Invariant Measure

      • Leszek Gawarecki, Vidyadhar Mandrekar
      Pages 233-283

  4. Back Matter

    Pages 285-291
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Keywords

About this book

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.

Reviews

From the reviews:

“The text is complete, accurate and a very clear introduction to the topic. … the book is a very nice and clear introduction to major methods in the study of infinite-dimensional stochastic differential equations. The book is not only appropriate for teaching purposes (it is designed for graduate students but due to its clear approach it can probably be used in undergraduate classes as well), but also a robust reference work for pure and applied mathematicians.” (Giorgio Fabbri, Mathematical Reviews, Issue 2012 a)

Authors and Affiliations

  • , Dept. Science and Mathematics, Kettering University, Flint, USA

    Leszek Gawarecki

  • , Dept. Statistics and Probability, Michigan State University, East Lansing, USA

    Vidyadhar Mandrekar

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