Large deviations for the stochastic functional integral equation with nonlocal condition

Purpose – The purpose of this paper is to study large deviations for the solution processes of a stochastic equation incorporated with the effects of nonlocal condition. Design/methodology/approach – A weak convergence approach is adopted to establish the Laplace principle, which is same as the large deviation principle in a Polish space. The sufficient condition for any family of solutions to satisfy the Laplace principle formulated by Budhiraja and Dupuis is used in this work. Findings – Freidlin–Wentzell type large deviation principle holds good for the solution processes of the stochastic functional integral equation with nonlocal condition. Originality/value – The asymptotic exponential decay rate of the solution processes of the considered equation towards its deterministic counterpart can be estimated using the established results

Large deviations for stochastic tidal dynamics equation

In this work, we study the large deviation principle of WentzellFreidlin type for the stochastic tidal dynamics equation with multiplicative noise in an open domain. The results are established by using a generalization of the Minty Browder method and also exploiting an inherent control theoretic structure of large deviation theory

Large deviations for stochastic Kuramoto–Sivashinsky equation with multiplicative noise

The Kuramoto–Sivashinsky equation is a nonlinear parabolic partial differential equation, which describes the instability and turbulence of waves in chemical reactions and laminar flames. The aim of this work is to prove the large deviation principle for the stochastic Kuramoto–Sivashinsky equation driven by multiplicative noise. To establish the large deviation principle, the weak convergence approach is used, which relies on proving basic qualitative properties of controlled versions of the original stochastic partial differential equation

http://www.aimspress.com/article/10.3934/Math.2017.2.336/fulltext.html

In this work we establish a Freidlin-Wentzell type large deviation principle for stochastic fractional integrodifferential equations by using the weak convergence approach. The compactness argument is proved on the solution space of corresponding skeleton equation and the weak convergence is done for Borel measurable functions whose existence is asserted from Yamada-Watanabe theorem. Examples are included which illustrate the theory and also depict the link between large deviations and optimal controllability

Large Deviations of Stochastic Tidal Dynamics Equations

In this work, we study the large deviation principle of WentzellFreidlin type for the stochastic tidal dynamics equation with multiplicative noise in an open domain. The results are established by using a generalization of the Minty Browder method and also exploiting an inherent control theoretic structure of large deviation theory

Analysis of stochastic neutral fractional functional differential equations

Abstract This work deals with the large deviation principle which studies the decay of probabilities of certain kind of extremely rare events. We consider stochastic neutral fractional functional differential equation with multiplicative noise and show large deviation principle for its solution processes in a suitable Polish space. The existence and uniqueness results are presented using the Picard iterative method, which is indeed essential for further analysis. The establishment of Freidlin–Wentzell type large deviation principle is solely based on the variational representation developed by Budhiraja and Dupuis in which the weak convergence technique is used to show the sufficient condition. Examples are provided to emphasize the theory