Singular Stochastic Differential Equations

AvAlexander S. Cherny,Hans-Jürgen Engelbert

Häftad, Engelska, 2004

Del i serien Lecture Notes in Mathematics

379 kr

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2004-12-02
Mått:155 x 235 x undefined mm
Format:Häftad
Språk:Engelska
Serie:Lecture Notes in Mathematics
Antal sidor:128
Förlag:Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
ISBN:9783540240075

Utforska kategorier

Matematik inom Naturvetenskap och teknik

Recensioner i media

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)

Innehållsförteckning

Introduction.- 1. Stochastic Differential Equations.- 2. One-Sided Classification of Isolated Singular Points.- 3. Two-Sided Classification of Isolated Singular Points.- 4. Classification at Infinity and Global Solutions.- 5. Several Special Cases.- Appendix A: Some Known Facts.- Appendix B: Some Auxiliary Lemmas.- Rferences.- Index of Notation.- Index of Terms.