scholarly journals Large Deviations for Stochastic Evolution Equations with Small Multiplicative Noise

2009 ◽  
Vol 61 (1) ◽  
pp. 27-56 ◽  
Author(s):  
Wei Liu
Keyword(s):  
Large Deviations ◽  
Multiplicative Noise ◽  
Evolution Equations ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations

scholarly journals On Jumps Stochastic Evolution Equations With Application of Homogenization and Large Deviations

2019 ◽  
Vol 11 (2) ◽  
pp. 125
Author(s):  
Cl´ement Manga ◽  
Alioune Coulibaly ◽  
Alassane Diedhiou
Keyword(s):  
Evolution Equation ◽  
Large Deviations ◽  
Evolution Equations ◽  
Stochastic Evolution Equation ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Large Deviations Principle ◽  
Viscosity Parameter ◽  
Two Parameters ◽  
And Diffusion

We consider a class of jumps and diffusion stochastic differential equations which are perturbed by to two parameters:  ε (viscosity parameter) and δ (homogenization parameter) both tending to zero. We analyse the problem taking into account the combinatorial effects of the two parameters  ε and δ . We prove a Large Deviations Principle estimate for jumps stochastic evolution equation in case that homogenization dominates.

scholarly journals Stochastic evolution equations with multiplicative noise

2015 ◽  
Vol 20 (0) ◽  
Author(s):  
Tijana Levajković ◽  
Stevan Pilipović ◽  
Dora Seleši ◽  
Milica Žigić
Keyword(s):  
Multiplicative Noise ◽  
Evolution Equations ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations

scholarly journals STOCHASTIC EVOLUUTION EQUATIONS WITH MONOTONE NONLINEARITY IN Lp SPACES

2019 ◽  
pp. 601
Author(s):  
Majid Amintorabi ◽  
Ruhollah Jahanipur
Keyword(s):  
Lipschitz Condition ◽  
Existence And Uniqueness ◽  
Multiplicative Noise ◽  
Evolution Equations ◽  
Type Inequality ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Nonlinear Part

In this paper, we study semilinear stochastic evolution equations with semimonotone nonlinearity and multiplicative noise in L p spaces for 2 ≤ p < ∞. We do not impose any coercivity or Lipschitz condition on the nonlinear part of equations. We prove the existence, uniqueness and measurability of the mild solutions.The proofs of the existence and uniqueness are based on a version of the Itˆ o type inequality which is stronger than analogues inequalities.

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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