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.

The Fifth IFIP Working Conference on Stochastic Differential Systems continues the traditional line of previous conferences in Kyoto (1976), Vilnjus (1978), Visegrad (1980), and Marseille-Luminy (1984) and focuses on topics of present research in the field of stochastic differential systems. Particular emphasis is laid on infinite-dimensional stochastic problems and random fields, especially on stochastic partial differential equations. The volume includes contributions to the study of stochastic equations and diffusion and their approximation, large deviations and stability of perturbed systems, stochastic control theory and filtering. There are also contributions to the study of some special problems in martingale theory and stochastic calculus. This volume is of special interest to researchers in stochastic processes, random fields, and control theory.