Limiting behavior of invariant measures of highly nonlinear stochastic retarded lattice systems
Yusen Lin, Dingshi Li
Abstract
<p style='text-indent:20px;'>This paper deals with the limiting behavior of invariant measures of the highly nonlinear stochastic retarded lattice systems. Although invariant measures of stochastic retarded lattice system has been studied recently, there is so far no result of invariant measure of stochastic retarded lattice systems with highly nonlinear drift or diffusion terms. We first show the existence of invariant measures of the systems. We then prove that any limit point of a tight sequence of invariant measures of the stochastic retarded lattice systems must be an invariant measure of the corresponding limiting system as the intensity of noise converges or the time-delay approaches zero.</p>
Topics & Concepts
Invariant measureLimitingInvariant (physics)Nonlinear systemMathematicsLattice (music)HomogeneousStatistical physicsMathematical analysisPure mathematicsApplied mathematicsPhysicsMathematical physicsCombinatoricsQuantum mechanicsEngineeringMechanical engineeringErgodic theoryAcousticsStability and Controllability of Differential EquationsStochastic processes and financial applicationsAdvanced Mathematical Modeling in Engineering