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© 2005

Singular Stochastic Differential Equations

  • Authors
Book

Part of the Lecture Notes in Mathematics book series (LNM, volume 1858)

Table of contents

  1. Front Matter
    Pages I-VIII
  2. Alexander S. Cherny, Hans-Jürgen Engelbert
    Pages 1-4
  3. Alexander S. Cherny, Hans-Jürgen Engelbert
    Pages 5-25
  4. Alexander S. Cherny, Hans-Jürgen Engelbert
    Pages 27-64
  5. Alexander S. Cherny, Hans-Jürgen Engelbert
    Pages 65-79
  6. Alexander S. Cherny, Hans-Jürgen Engelbert
    Pages 81-91
  7. Alexander S. Cherny, Hans-Jürgen Engelbert
    Pages 93-103
  8. Alexander S. Cherny, Hans-Jürgen Engelbert
    Pages 105-118
  9. Alexander S. Cherny, Hans-Jürgen Engelbert
    Pages 119-121
  10. Alexander S. Cherny, Hans-Jürgen Engelbert
    Pages 123-128

About this book

Introduction

The authors introduce, in this research monograph on stochastic differential equations, a class of points termed isolated singular points. Stochastic differential equations possessing such points (called singular stochastic differential equations here) arise often in theory and in applications. However, known conditions for the existence and uniqueness of a solution typically fail for such equations. The book concentrates on the study of the existence, the uniqueness, and, what is most important, on the qualitative behaviour of solutions of singular stochastic differential equations. This is done by providing a qualitative classification of isolated singular points, into 48 possible types.

Keywords

classification of solutions equation existence of solution isolated singular points stochastic differential equation stochastic differential equations uniqueness of solution

Bibliographic information

  • Book Title Singular Stochastic Differential Equations
  • Authors Alexander S. Cherny
    Hans-Jürgen Engelbert
  • Series Title Lecture Notes in Mathematics
  • Series Abbreviated Title LNM
  • DOI https://doi.org/10.1007/b104187
  • Copyright Information Springer-Verlag Berlin Heidelberg 2005
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Softcover ISBN 978-3-540-24007-5
  • eBook ISBN 978-3-540-31560-5
  • Series ISSN 0075-8434
  • Series E-ISSN 1617-9692
  • Edition Number 1
  • Number of Pages VIII, 128
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Probability Theory and Stochastic Processes
  • Buy this book on publisher's site
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Reviews

From the reviews:

"The main aim of this outstanding research monograph on stochastic differential equations is to introduce a class of points termed isolated singular points. … The book studies the existence, the uniqueness, and the qualitative behaviour of solutions of singular stochastic differential equations." (Pavel Gapeev, Zentralblatt MATH, Vol. 1071, 2005)

"Cherny and Engelbert’s book is a research monograph, devoted predominantly to the author’s recent deep results, it is written very carefully, in a lucid and precise way, and contains many illustrating examples. The authors have managed to keep it surprisingly self-contained. In my opinion, it is necessary reading for everybody who wishes to understand one-dimensional diffusions thoroughly." (Jan I. Seidler, Mathematical Reviews, Issue 2005 j)