scholarly journals An averaging principle for stochastic evolution equations. I.

1990 ◽  
Vol 115 (3) ◽  
pp. 240-263 ◽  
Author(s):  
Jan Seidler ◽  
Ivo Vrkoč
Keyword(s):  
Evolution Equations ◽  
Averaging Principle ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations

scholarly journals An averaging principle for stochastic evolution equations. II.

1991 ◽  
Vol 116 (2) ◽  
pp. 191-224 ◽  
Author(s):  
Bohdan Maslowski ◽  
Jan Seidler ◽  
Ivo Vrkoč
Keyword(s):  
Evolution Equations ◽  
Averaging Principle ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations

Averaging principle for impulsive stochastic partial differential equations

2020 ◽  
pp. 2150014
Author(s):  
Jiankang Liu ◽  
Wei Xu ◽  
Qin Guo
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Evolution Equations ◽  
Sufficient Conditions ◽  
Original System ◽  
Averaging Principle ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Partial Differential

This paper focuses on systems of stochastic partial differential equations with impulse effects. We establish an averaging principle such that the solution to the complex original nonlinear impulsive stochastic evolution equations can be approximated by that to the more simplified averaged stochastic evolution equations without impulses. By adopting stochastic analysis theory, semigroup approach and inequality technique, sufficient conditions are formulated and the mean square convergence is proved. This ensures that we can concentrate on the averaged system instead of the original system, thus providing a solution for reduction of complexity.

scholarly journals Smoothness of solutions of stochastic evolution equations and the existence of a filtering transition density

1981 ◽  
Vol 84 ◽  
pp. 195-208 ◽  
Author(s):  
B. L. Rozovskii ◽  
A. Shimizu
Keyword(s):  
Evolution Equations ◽  
Transition Density ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Smoothness Of Solutions

In this paper, we shall discuss the smoothness of solutions of stochastic evolution equations, which has been investigated in N. V. Krylov and B. L. Rozovskii [2] [3], to establish the existence of a filtering transition density.

scholarly journals On Almost Automorphic Mild Solutions for Nonautonomous Stochastic Evolution Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-25 ◽  
Author(s):  
Jing Cui ◽  
Litan Yan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Banach Fixed Point Theorem ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Almost Automorphic ◽  
Composition Theorem

We consider a class of nonautonomous stochastic evolution equations in real separable Hilbert spaces. We establish a new composition theorem for square-mean almost automorphic functions under non-Lipschitz conditions. We apply this new composition theorem as well as intermediate space techniques, Krasnoselskii fixed point theorem, and Banach fixed point theorem to investigate the existence of square-mean almost automorphic mild solutions. Some known results are generalized and improved.

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