Wong-Zakai approximations of stochastic lattice systems driven by long-range interactions and multiplicative white noises
Yi‐Ju Chen, Xiaohu Wang, Kenan Wu
Abstract
<p style='text-indent:20px;'>In this paper, we study the Wong-Zakai approximations of a stochastic lattice differential equation with long-range interactions and multiplicative white noise at each node. We first prove the existence and uniqueness of pullback random attractors for lattice system driven by multiplicative white noises as well as the corresponding Wong-Zakai approximate system. Then, we prove the convergence of solutions and the upper semicontinuity of random attractors for the Wong-Zakai approximate system as the size of approximation approaches zero.</p>
Topics & Concepts
Multiplicative functionMathematicsMultiplicative noiseLattice (music)UniquenessWhite noiseStochastic differential equationAttractorApplied mathematicsMathematical analysisComputer sciencePhysicsStatisticsAcousticsSignal transfer functionDigital signal processingComputer hardwareAnalog signalStability and Controllability of Differential EquationsAdvanced Mathematical Modeling in EngineeringNonlinear Differential Equations Analysis