Invariance principles for G-brownian-motion-driven stochastic differential equations and their applications to G-stochastic control
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866916553985884160 |
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| author | Peng, Xiaoxiao Zhou, Shijie Lin, Wei Mao, Xuerong |
| author_facet | Peng, Xiaoxiao Zhou, Shijie Lin, Wei Mao, Xuerong |
| contents | The G-Brownian-motion-driven stochastic differential equations (G-SDEs) as well as the G-expectation, which were seminally proposed by Peng and his colleagues, have been extensively applied to describing a particular kind of uncertainty arising in real-world systems modeling. Mathematically depicting long-time and limit behaviors of the solution produced by G-SDEs is beneficial to understanding the mechanisms of system's evolution. Here, we develop a new G-semimartingale convergence theorem and further establish a new invariance principle for investigating the long-time behaviors emergent in G-SDEs. We also validate the uniqueness and the global existence of the solution of G-SDEs whose vector fields are only locally Lipchitzian with a linear upper bound. To demonstrate the broad applicability of our analytically established results, we investigate its application to achieving G-stochastic control in a few representative dynamical systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_08366 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Invariance principles for G-brownian-motion-driven stochastic differential equations and their applications to G-stochastic control Peng, Xiaoxiao Zhou, Shijie Lin, Wei Mao, Xuerong Probability Dynamical Systems The G-Brownian-motion-driven stochastic differential equations (G-SDEs) as well as the G-expectation, which were seminally proposed by Peng and his colleagues, have been extensively applied to describing a particular kind of uncertainty arising in real-world systems modeling. Mathematically depicting long-time and limit behaviors of the solution produced by G-SDEs is beneficial to understanding the mechanisms of system's evolution. Here, we develop a new G-semimartingale convergence theorem and further establish a new invariance principle for investigating the long-time behaviors emergent in G-SDEs. We also validate the uniqueness and the global existence of the solution of G-SDEs whose vector fields are only locally Lipchitzian with a linear upper bound. To demonstrate the broad applicability of our analytically established results, we investigate its application to achieving G-stochastic control in a few representative dynamical systems. |
| title | Invariance principles for G-brownian-motion-driven stochastic differential equations and their applications to G-stochastic control |
| topic | Probability Dynamical Systems |
| url | https://arxiv.org/abs/2309.08366 |