Wong–Zakai approximations of the non-autonomous stochastic FitzHugh–Nagumo system on RN in higher regular spaces
Wenqiang Zhao
Abstract
In this paper, we consider the Wong–Zakai approximations of a non-autonomous stochastic FitzHugh–Nagumo system driven by a multiplicative white noise with an arbitrary intensity. The convergence of solutions of the path-wise deterministic system to that of the corresponding stochastic system is established in higher regular spaces by means of a new iteration technique and an optimal multiplier at different stages. Furthermore, we prove that the random attractor of the path-wise deterministic system converges to that of the non-autonomous stochastic FitzHugh–Nagumo system in higher regular spaces when the size of approximation vanishes, with much looser conditions on the nonlinearity.
Topics & Concepts
MathematicsMultiplicative noiseMultiplicative functionAttractorApplied mathematicsNonlinear systemConvergence (economics)White noiseMultiplier (economics)Mathematical analysisComputer scienceEconomicsStatisticsMacroeconomicsDigital signal processingPhysicsEconomic growthSignal transfer functionComputer hardwareQuantum mechanicsAnalog signalStability and Controllability of Differential EquationsAdvanced Mathematical Modeling in EngineeringStochastic processes and financial applications