Lecture Notes in Mathematics

Singular Stochastic Differential Equations

Authors: Cherny, Alexander S., Engelbert, Hans-Jürgen

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About this book

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.

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)


Table of contents (9 chapters)

  • Introduction

    Cherny, Alexander S. (et al.)

    Pages 1-4

  • 1. Stochastic Differential Equations

    Cherny, Alexander S. (et al.)

    Pages 5-25

  • 2. One-Sided Classification of Isolated Singular Points

    Cherny, Alexander S. (et al.)

    Pages 27-64

  • 3. Two-Sided Classification of Isolated Singular Points

    Cherny, Alexander S. (et al.)

    Pages 65-79

  • 4. Classification at Infinity and Global Solutions

    Cherny, Alexander S. (et al.)

    Pages 81-91

Buy this book

eBook $34.99
price for USA (gross)
  • ISBN 978-3-540-31560-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.95
price for USA
  • ISBN 978-3-540-24007-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Singular Stochastic Differential Equations
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1858
Copyright
2005
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-31560-5
DOI
10.1007/b104187
Softcover ISBN
978-3-540-24007-5
Series ISSN
0075-8434
Edition Number
1
Number of Pages
VIII, 128
Topics