We study stochastic differential equations with a small perturbation parameter. Under the dissipative condition on the drift coefficient and the local Lipschitz condition on the drift and diffusion coefficients we prove the existence and uniqueness result for the perturbed SDE, also the convergence result for the solution of the perturbed system to the solution of the unperturbed system when the perturbation parameter approaches zero. We consider the application of the above-mentioned results to the Cauchy problem and the transport equations

DIFFUSION APPROXIMATION FOR TRANSPORT EQUATIONS WITH DISSIPATIVE DRIFTS

Di Persio Luca;Vardanyan Viktorya
2022-01-01

Abstract

We study stochastic differential equations with a small perturbation parameter. Under the dissipative condition on the drift coefficient and the local Lipschitz condition on the drift and diffusion coefficients we prove the existence and uniqueness result for the perturbed SDE, also the convergence result for the solution of the perturbed system to the solution of the unperturbed system when the perturbation parameter approaches zero. We consider the application of the above-mentioned results to the Cauchy problem and the transport equations
2022
Cauchy problem, Diffusion process, Dissipative drift, Local lipschitz condition, Perturbation parameter, Transport equation
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11562/1073087
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