Propagation of Chaos for Weakly Interacting Mild Solutions to Stochastic Partial Differential Equations

Mild Solutions of Neutral Stochastic Partial Functional Differential Equations

The Yamada-Watanabe theorem for mild solutions to stochastic partial differential equations

We prove the Yamada-Watanabe Theorem for semilinear stochastic partial differential equations with path-dependent coefficients. The so-called “method of the moving frame” allows us to reduce the proof to the Yamada-Watanabe Theorem for stochastic differential equations in infinite dimensions.

Almost Automorphic Mild Solutions to Fractional Partial Difference-differential Equations

We study existence and uniqueness of almost automorphic solutions for nonlinear partial difference-differential equations modeled in abstract form as (∗) ∆u(n) = Au(n+ 1) + f(n, u(n)), n ∈ Z, for 0 < α ≤ 1 where A is the generator of a C0-semigroup defined on a Banach space X, ∆ denote fractional difference in Weyl-like sense and f satisfies Lipchitz conditions of global and local type. We intr...

Exponential stability of mild solutions to impulsive stochastic neutral partial differential equations with memory

*Correspondence: [email protected]; [email protected] 1School of Mathematics & Computer Science, Wuhan Polytechnic University, Wuhan, Hubei, China 2School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan, Hubei, China Abstract In this paper, we study the exponential stability in the pth moment of mild solutions to impulsive stochastic neutral partial differential e...

Existence and Stability of Mild Solutions to Impulsive Stochastic Neutral Partial Functional Differential Equations

In this article, we study a class of impulsive stochastic neutral partial functional differential equations in a real separable Hilbert space. By using Banach fixed point theorem, we give sufficient conditions for the existence and uniqueness of a mild solution. Also the exponential p-stability of a mild solution and its sample paths are obtained.