Stochastic evolution equations driven by nuclear-space-valued martingales

1988 ◽  
Vol 17 (1) ◽  
pp. 237-272 ◽  
Author(s):  
G. Kallianpur ◽  
V. Perez-Abreu
Keyword(s):  
Evolution Equations ◽  
Nuclear Space ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations

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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