Reflected Stochastic Differential Equations Driven by G-Brownian Motion with Nonlinear Constraints
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915953203216384 |
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| author | Li, Hanwu |
| author_facet | Li, Hanwu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_22130 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Reflected Stochastic Differential Equations Driven by G-Brownian Motion with Nonlinear Constraints Li, Hanwu Probability 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. |
| title | Reflected Stochastic Differential Equations Driven by G-Brownian Motion with Nonlinear Constraints |
| topic | Probability |
| url | https://arxiv.org/abs/2604.22130 |