References & Citations
Mathematics > Probability
Title: Stochastic Differential Equations Driven by G-Brownian Motion with Mean Reflections
(Submitted on 15 Jun 2023 (v1), last revised 26 Apr 2024 (this version, v2))
Abstract: In this paper, we study the mean reflected stochastic differential equations driven by G- Brownian motion, where the constraint depends on the distribution of the solution rather than on its paths. Well-posedness is achieved by first investigating the Skorokhod problem with mean reflection under the 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. Additionally, a new technique is proposed to prove the first propagation of chaos result for mean reflected G-SDEs, overcoming challenges posed by the nonlinearity of G- expectation and the non-deterministic nature of the quadratic variation of G-Brownian motion.
Submission history
From: Hanwu Li [view email][v1] Thu, 15 Jun 2023 08:14:14 GMT (19kb)
[v2] Fri, 26 Apr 2024 13:22:12 GMT (29kb)
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