Singular Stochastic Differential Equations

Alexander S. Cherny, Hans-Jürgen Engelbert (auth.)3540240071, 9783540240075

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.

Table of contents :
Introduction….Pages 1-4
1. Stochastic Differential Equations….Pages 5-25
2. One-Sided Classification of Isolated Singular Points….Pages 27-64
3. Two-Sided Classification of Isolated Singular Points….Pages 65-79
4. Classification at Infinity and Global Solutions….Pages 81-91
5. Several Special Cases….Pages 93-103
Appendix….Pages 105-118
References….Pages 119-121
Index of Notation and Index of Terms….Pages 123-128