The existence and uniqueness of solutions of nuclear space-valued stochastic differential equations driven by poisson random measures

Publisher Website
Google Scholar
Abstract
In this paper, we study stochastic differential equations (SDE's) on duals of nuclear spaces driven by Poisson random measures. The existence of a weak solution is obtained by the Galerkin method. For uniqueness, a class of :-valued processes which are called Good processes are introduced. An equivalence relation is established between SDE's driven by Poisson random measures and those by Good processes. The uniqueness is established by extending the Yamada-Watanabe argument to the SDE's driven by Good processes. This is an extension to discontinuous infinite dimensional SDE's of work done by G. Kallianpur, I. Mitoma and R. Wolpert for nuclear space valued diffusions.