| Autor: |
XIAOXIAO PENG, SHIJIE ZHOU, WEI LIN, XUERONG MAO |
| Předmět: |
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| Zdroj: |
SIAM Journal on Control & Optimization; 2024, Vol. 62 Issue 3, p1569-1589, 21p |
| Abstrakt: |
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 Lipschitzian 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. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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