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

Large deviation principle for semilinear stochastic evolution equations with Poisson noise

2017 ◽  
Vol 20 (02) ◽  
pp. 1750009
Author(s):  
Hassan Dadashi
Keyword(s):  
Evolution Equations ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Functional Differential Equations ◽  
Random Measure ◽  
Poisson Noise ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Deviation Principle ◽  
Wide Range

We demonstrate the large deviation principle in the small noise limit for the mild solution of semilinear stochastic evolution equations with monotone nonlinearity and multiplicative Poisson noise. A recently developed method in studying the large deviation principle, weak convergent method, is employed. We apply the result obtained by Budhiraja et al.,7 that reveals the variational representation of exponential integrals w.r.t. the Poisson random measure. Our framework covers a wide range of parabolic, hyperbolic and functional differential equations. We give some examples to illustrate the applications of our results.

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
Sign in / Sign up

Export Citation Format

Share Document