Singular Stochastic Differential Equations
Authors: Cherny, Alexander S., Engelbert, Hans-Jürgen
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- About this book
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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
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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)
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Introduction
Pages 1-4
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1. Stochastic Differential Equations
Pages 5-25
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2. One-Sided Classification of Isolated Singular Points
Pages 27-64
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3. Two-Sided Classification of Isolated Singular Points
Pages 65-79
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4. Classification at Infinity and Global Solutions
Pages 81-91
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Table of contents (9 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Singular Stochastic Differential Equations
- Authors
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- Alexander S. Cherny
- Hans-Jürgen Engelbert
- 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
