Probabilistic approach to singular perturbations of viscosity solutions to nonlinear parabolic PDEs

Mingshang Hu and Falei Wang

Stochastic Processes and their Applications, 2021, vol. 141, issue C, 139-171

Abstract: In this paper, we prove a convergence theorem for singular perturbations problems for a class of fully nonlinear parabolic partial differential equations (PDEs) with ergodic structures. The limit function is represented as the viscosity solution to a fully nonlinear degenerate PDEs. Our approach is mainly based on G-stochastic analysis argument. As a byproduct, we also establish the averaging principle for stochastic differential equations driven by G-Brownian motion (G-SDEs) with two time-scales. The results extend Khasminskii’s averaging principle to nonlinear case.

Keywords: Singular perturbation; Averaging principle; Nonlinear PDE; G-Brownian motion (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.spa.2021.07.006

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