scholarly journals Freidlin-Wentzell’s Large Deviations for Stochastic Evolution Equations with Poisson Jumps

2016 ◽  
Vol 06 (10) ◽  
pp. 676-694 ◽  
Author(s):  
Huiyan Zhao ◽  
Siyan Xu
Keyword(s):  
Large Deviations ◽  
Evolution Equations ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Poisson Jumps

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.

THE EXISTENCE AND ASYMPTOTIC BEHAVIOUR OF MILD SOLUTIONS TO STOCHASTIC EVOLUTION EQUATIONS WITH INFINITE DELAYS DRIVEN BY POISSON JUMPS

2009 ◽  
Vol 09 (02) ◽  
pp. 217-229 ◽  
Author(s):  
TAKESHI TANIGUCHI ◽  
JIAOWAN LUO
Keyword(s):  
Initial Function ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Jump Processes ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Poisson Jumps ◽  
Infinite Delays ◽  
Poisson Jump ◽  
Exponentially Stable

In this paper we consider a sufficient condition for mild solutions to exist and to be almost surely exponentially stable or exponentially ultimate bounded in mean square for the following stochastic evolution equation with infinite delays driven by Poisson jump processes: [Formula: see text] with an initial function X(s) = φ (s), -∞ < s ≤ 0, where φ : (-∞, 0] → H is a càdlàg function with [Formula: see text].

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.

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