Stochastic dynamical systems and processes with discontinuous sample paths

Chapter 1 we use a Poisson stochastic measure to establish a method of localizing, and a change of chart formula for, a class of stochastic differential equations with discontinuous sample paths. This is based on Gikhman and Skorohod [4]. In Chapter 2 we use essentially the method of Elworthy [2], to construct a unique, maximal solution to a stochastic differential equation defined on a manifold M. Chapter 3 establishes some properties of solutions of the equation. In particular if M is compact, then the solutions have infinite explosion time. We evaluate the infinitesimal generator of the process. By defining stochastic development of a-stable processes on the tangent space, we produce a process on the manifold which, as is shown in Section 6, is not a-stable on M