Singular Stochastic Differential Equations
Cherny, Alexander S.
Singular Stochastic Differential Equations [electronic resource] / by Alexander S. Cherny, Hans-Jürgen Engelbert. - VIII, 128 p. online resource. - Lecture Notes in Mathematics, 1858 0075-8434 ; . - Lecture Notes in Mathematics, 1858 .
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.
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.
9783540315605
10.1007/b104187 doi
Distribution (Probability theory.
Probability Theory and Stochastic Processes.
QA273.A1-274.9 QA274-274.9
519.2
Singular Stochastic Differential Equations [electronic resource] / by Alexander S. Cherny, Hans-Jürgen Engelbert. - VIII, 128 p. online resource. - Lecture Notes in Mathematics, 1858 0075-8434 ; . - Lecture Notes in Mathematics, 1858 .
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.
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.
9783540315605
10.1007/b104187 doi
Distribution (Probability theory.
Probability Theory and Stochastic Processes.
QA273.A1-274.9 QA274-274.9
519.2