Yamada-Watanabe Theorem for Stochastic Evolution Equation Driven by Poisson Random Measure

Huiyan Zhao

doi:10.1155/2014/982190

Abstract

The purpose of this paper is to give a detailed proof of Yamada-Watanabe theorem for stochastic evolution equation driven by pure Poisson random measure.

Highlights

The main purpose of this paper is to establish the YamadaWatanabe theory of uniqueness and existence of solutions of stochastic evolution equation driven by pure Poisson random measure in the variational approach
The classical paper [1] has initiated a comprehensive study of relations between different types of uniqueness and existence arising in the study of SDEs and the study is still alive today
In this paper we are concerned with the similar question for stochastic evolution equation driven by Poisson random measure by using the method of Yamada and Watanabe

Summary

Introduction

The main purpose of this paper is to establish the YamadaWatanabe theory of uniqueness and existence of solutions of stochastic evolution equation driven by pure Poisson random measure in the variational approach. In this paper we are concerned with the similar question for stochastic evolution equation driven by Poisson random measure by using the method of Yamada and Watanabe. Rockner et al [7] proved similar result for stochastic evolution equation in Banach space driven by cylindrical Wiener process under the variational framework. We will consider the following stochastic evolution equation driven by pure Poisson random measure under the variational framework: t. It is well known that a Brownian motion can be treated as a canonical map on C([0, ∞); Rn) or C([0, ∞); H) (for some Hilbert space H), while for jump-case we have to work on the configuration space N (see Section 2) for Poisson random measure.

Framework and Definitions

The Main Result and Its Proof

Conclusions

Conflict of Interests