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Mathematics - Probability Theory and Stochastic Processes | Singular Stochastic Differential Equations

Singular Stochastic Differential Equations

Series: Lecture Notes in Mathematics, Vol. 1858

Cherny, Alexander S., Engelbert, Hans-Jürgen

2005, VIII, 128 p.

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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.

Content Level » Research

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

Related subjects » Probability Theory and Stochastic Processes

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