scholarly journals On the Equivalence of Solutions for a Class of Stochastic Evolution Equations in a Banach Space

2014 ◽  
Vol 78 (4) ◽  
pp. 451-481 ◽  
Author(s):  
Mariusz Górajski
Keyword(s):  
Banach Space ◽  
Evolution Equations ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations

scholarly journals Uniform large deviation principles for Banach space valued stochastic evolution equations

2019 ◽  
Vol 372 (12) ◽  
pp. 8363-8421
Author(s):  
Michael Salins ◽  
Amarjit Budhiraja ◽  
Paul Dupuis
Keyword(s):  
Banach Space ◽  
Evolution Equations ◽  
Large Deviation ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Large Deviation Principles

ALMOST PERIODIC SOLUTIONS TO STOCHASTIC EVOLUTION EQUATIONS ON BANACH SPACES

2013 ◽  
Vol 13 (03) ◽  
pp. 1250027 ◽  
Author(s):  
P. CREWE
Keyword(s):  
Banach Space ◽  
Periodic Solutions ◽  
Banach Spaces ◽  
Evolution Equations ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Stochastic Integration ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Semigroup Generator

We prove the existence of almost periodic solutions to a class of abstract stochastic evolution equations on a Banach space E, [Formula: see text] Both autonomous (A is a C0-semigroup generator) and non-autonomous (A(t) satisfies conditions of Acquistapace–Terreni and generates a strongly continuous evolution family) cases are studied. Results are based on the theory of stochastic integration on Banach spaces of van Neerven and Weis and R-boundedness estimates for semigroups and evolution families due to Hytönen and Veraar. An example is given for a non-autonomous second order boundary value problem on a domain in ℝd.

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.

On nonlinear stochastic evolution equations∗

1996 ◽  
Vol 14 (3) ◽  
pp. 303-311 ◽  
Author(s):  
Jai Heui Kim
Keyword(s):  
Evolution Equations ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations

scholarly journals Approximate Controllability of Impulsive Stochastic Evolution Equations

2009 ◽  
Vol 52 (3) ◽  
pp. 381-393 ◽  
Author(s):  
Rathinasamy Sakthivel
Keyword(s):  
Approximate Controllability ◽  
Evolution Equations ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations

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

scholarly journals Freidlin–Wentzell's large deviations for stochastic evolution equations

2008 ◽  
Vol 254 (12) ◽  
pp. 3148-3172 ◽  
Author(s):  
Jiagang Ren ◽  
Xicheng Zhang
Keyword(s):  
Large Deviations ◽  
Evolution Equations ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations
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