Discrete and Continuous Dynamical Systems · 2015 · 10 citations · 16 references
EngineeringMechanical EngineeringMemoryProbability TheoryStochastic ProcessesContinuous-time Stochastic ProcessesDiffusion ProcessesLarge DeviationsLimit TheoremsStochastic CalculusStochastic Differential EquationsDirichlet Boundary ConditionsDirichlet ConditionsFreidlin - Wentzell TheoryHeat EquationLarge Deviation InequalitiesLarge Deviation PrinciplesLarge Deviations PrincipleWeak Convergence Of Stochastic Processes
In this work, using the weak convergence argument, we prove a Freidlin-Wentzell's large deviation principle fora class of stochastic heat equations with memory and Dirichlet boundary conditions, where the nonlinear termis allowed to be of polynomial growth.
16
ON SMALL RANDOM PERTURBATIONS OF DYNAMICAL SYSTEMS
A. D. Ventsel’, Mark Freidlin · Russian Mathematical Surveys · 1970 · 397 citations