Attractors of probability measures for semilinear stochastic evolution equations

1992 ◽  
Vol 10 (2) ◽  
pp. 205-212 ◽  
Author(s):  
Hiroaki Morimoto
Keyword(s):  
Evolution Equations ◽  
Probability Measures ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations

scholarly journals Fractional Measure-dependent Nonlinear Second-order Stochastic Evolution Equations with Poisson Jumps

2018 ◽  
Vol 5 (1) ◽  
pp. 59-75 ◽  
Author(s):  
Mark A. McKibben ◽  
Micah Webster
Keyword(s):  
Evolution Equations ◽  
Mild Solutions ◽  
Stability Result ◽  
Growth Conditions ◽  
Second Order ◽  
Probability Measures ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Poisson Jumps ◽  
Fractional Measure

Abstract This paper focuses on a nonlinear second-order stochastic evolution equations driven by a fractional Brownian motion (fBm) with Poisson jumps and which is dependent upon a family of probability measures. The global existence of mild solutions is established under various growth conditions, and a related stability result is discussed. An example is presented to illustrate the applicability of the theory.

scholarly journals On a Class of Measure-Dependent Stochastic Evolution Equations Driven by fBm

2007 ◽  
Vol 2007 ◽  
pp. 1-26 ◽  
Author(s):  
Eduardo Hernandez ◽  
David N. Keck ◽  
Mark A. McKibben
Keyword(s):  
Hilbert Space ◽  
Brownian Motion ◽  
Existence And Uniqueness ◽  
Continuous Dependence ◽  
Evolution Equations ◽  
Separable Hilbert Space ◽  
Probability Measures ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Real Separable Hilbert Space

We investigate a class of abstract stochastic evolution equations driven by a fractional Brownian motion (fBm) dependent upon a family of probability measures in a real separable Hilbert space. We establish the existence and uniqueness of a mild solution, a continuous dependence estimate, and various convergence and approximation results. Finally, the analysis of three examples is provided to illustrate the applicability of the general theory.

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.

scholarly journals Stochastic evolution equations with random generators

1998 ◽  
Vol 26 (1) ◽  
pp. 149-186 ◽  
Author(s):  
Jorge A. Le{\'o}n ◽  
David Nualart
Keyword(s):  
Evolution Equations ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Random Generators
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