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

2017/08/07 by Hu, Mingshang, Ji, Xiaojun, Liu, Guomin · 1 citation
#60H10 #60H30 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1708.02186

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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• Squared Bessel processes under nonlinear expectation

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