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

Mingshang Hu; Xiaojun Ji; Guomin Liu

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

Probability 2017-11-29 v2

Authors: Mingshang Hu , Xiaojun Ji , Guomin Liu

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.

Keywords

G-Brownian motion stochastic differential equations strong Markov property conditional G-expectation optional time

Cite

@article{arxiv.1708.02186,
  title  = {On the strong Markov property for stochastic differential equations driven by $G$-Brownian motion},
  author = {Mingshang Hu and Xiaojun Ji and Guomin Liu},
  journal= {arXiv preprint arXiv:1708.02186},
  year   = {2017}
}

Comments

Corrected some typos

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