On the strong Markov property for stochastic differential equations driven by $G$-Brownian motion

Mingshang Hu; Xiaojun Ji; Guomin Liu

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arXiv · 1708.02186

On the strong Markov property for stochastic differential equations driven by $G$-Brownian motion

Mingshang Hu·Xiaojun Ji·Guomin Liu

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Abstract

In this paper we study the stochastic differential equations driven by $G$-Brownian motion ($G$-SDEs for short). We extend the notion of conditional $G$-expectation from deterministic time to the more general optional time situation. Then, via this conditional expectation, we develop the strong Markov property for $G$-SDEs. In particular, we obtain the strong Markov property for $G$-Brownian motion. Some applications including the reflection principle for $G$-Brownian motion are also provided.

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BibTeX RIS

Mingshang Hu, Xiaojun Ji, Guomin Liu. 2017-08-07. On the strong Markov property for stochastic differential equations driven by $G$-Brownian motion. https://arxiv.org/abs/1708.02186

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