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.

中文翻译：

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G-布朗运动驱动的随机微分方程的强马尔可夫性质

在本文中，我们研究了由$G$-Brownian 运动（简称$G$-SDEs）驱动的随机微分方程。我们将条件 $G$-期望的概念从确定性时间扩展到更一般的可选时间情况。然后，通过这个条件期望，我们开发了 $G$-SDE 的强马尔可夫性质。特别是，我们获得了 $G$-布朗运动的强马尔可夫性质。还提供了一些应用，包括 $G$-布朗运动的反射原理。