Reflected Stochastic Differential Equations Driven by G-Brownian Motion with Nonlinear Constraints

Hanwu Li

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arXiv · 2604.22130

Reflected Stochastic Differential Equations Driven by G-Brownian Motion with Nonlinear Constraints

Hanwu Li

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Abstract

In this paper, we study the reflected stochastic differential equations driven by G-Brownian motion (reflected G-SDEs) with two nonlinear constraints. With the help of the Skorokhod problem with nonlinear constraints, we first study the doubly reflected G-Brownian motion, which is constructed pathwise and lies in the same G-expectation space as the G-Brownian motion. For the reflected G-SDE, the uniqueness is derived from some a priori estimate and the existence is obtained by a Picard iteration method. The comparison theorem of the solution and the individual constraining processes are provided.

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Hanwu Li. 2026-04-24. Reflected Stochastic Differential Equations Driven by G-Brownian Motion with Nonlinear Constraints. https://arxiv.org/abs/2604.22130

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