Abstract
We consider a class of neutral stochastic partial differential equations driven by an α-stable process. We prove the existence and uniqueness of the mild solution to the equation by the Banach fixed-point theorem under some suitable assumptions. Sufficient conditions for the stability in the distribution of the mild solution are derived.MSC:39A11, 37H10.
Highlights
1 Introduction The theory of stochastic partial differential equations has been widely applied in scientific fields such as physics, mechanical engineering, and economics
The study of stochastic neutral functional differential equations has received a great deal of attention in recent years
For the case of stochastic partial differential equations, we refer to Bao et al [, ]
Summary
The theory of stochastic partial differential equations has been widely applied in scientific fields such as physics, mechanical engineering, and economics. Bao et al [ ] extended the existence and uniqueness of mild solutions to a class of more general stochastic neutral partial functional differential equations under non-Lipschitz conditions. Yuan et al [ ] discussed a class of stochastic differential delay equation with Markovian switching, where the sufficient conditions of stability in the distribution were established. It seems that little is known about the stability in the distribution of the neutral stochastic partial differential equations driven by an α-stable process, and there are few systematic works so far in which the noise source is an α-stable process as well. We study the existence, uniqueness, and stability in the distribution of mild solutions for the following neutral stochastic differential equation with finite delay:.
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