Stochastic Differential Equations Driven by G-Brownian Motion with Mean Reflections

Hanwu Li; Ning Ning

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arXiv · 2306.08931

Stochastic Differential Equations Driven by G-Brownian Motion with Mean Reflections

Hanwu Li·Ning Ning

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Abstract

In this paper, we study the mean reflected stochastic differential equations driven by G-Brownian motion, where the constraint depends on the expectation of the solution rather than on its paths. Well-posedness is achieved by first investigating the Skorokhod problem with mean reflection under G-expectation. Two approaches to constructing the solution are introduced, both offering insights into desired properties and aiding in the application of the contraction mapping method.

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Hanwu Li, Ning Ning. 2023-06-15. Stochastic Differential Equations Driven by G-Brownian Motion with Mean Reflections. https://arxiv.org/abs/2306.08931

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