Abstract
In this paper, we shall discuss the uniqueness ”pathwise uniqueness” of the solutions of stochastic partial differential equations (SPDEs) with non-local initial condition,We shall use the Yamada-Watanabe condition for ”pathwise uniqueness” of the solutions of the stochastic differential equation; this condition is weaker than the usual Lipschitz condition. The proof is based on Bihari’sinequality.
Highlights
Our main result is using the Yamada-Watanabe condition, which relaxes the Lipschitz condition for the pathwise uniqueness of the solutions of stochastic differential equation in [3],[4] in the proof the pathwise uniqueness of (1)
Before starting the main theorem, we start with some definitions and theorems necessary for the sequel
The triple (Ω, P) consisting of a sample space Ω, the σ-algebra of subsets of Ω and a probability measure P defined on is known as a probability space
Summary
Our main result is using the Yamada-Watanabe condition, which relaxes the Lipschitz condition for the pathwise uniqueness of the solutions of stochastic differential equation in [3],[4] in the proof the pathwise uniqueness of (1). Before starting the main theorem, we start with some definitions and theorems necessary for the sequel
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