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

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:131

Article

Hu, Mingshang¹  Ji, Xiaojun²  Liu, Guomin³ 

[1] Shandong Univ, Zhongtai Secur Inst Financial Studies, Jinan, Peoples R China

[2] Shandong Univ, Sch Math, Jinan, Peoples R China

[3] Fudan Univ, Sch Math Sci, Shanghai, Peoples R China

关键词: G-expectation;    Strong Markov property;    Stochastic differential equations;    G-Brownian motion;    Reflection principle;   

DOI  :  10.1016/j.spa.2020.09.015

来源: Elsevier

【 摘 要 】

The objective of this paper is to study the strong Markov property for the stochastic differential equations driven by G-Brownian motion (G-SDEs for short). We first extend the deterministic-time conditional G-expectation to optional times. The strong Markov property for G-SDEs is then obtained by Kolmogorov's criterion for tightness. In particular, for any given optional time tau and G-Brownian motion B, the reflection principle for B holds and (B tau+t - B-t)(t >= 0) is still a G-Brownian motion. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

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