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

• Published in: Stochastic processes and their applications Vol. 131; pp. 417 - 453
• Main Authors: Hu, Mingshang, Ji, Xiaojun, Liu, Guomin
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.01.2021
• Subjects: [formula omitted]-Brownian motion; [formula omitted]-expectation; Reflection principle; Stochastic differential equations; Strong Markov property; G-expectation; 60H10; Stochastic differential equations; Reflection principle; 60H30; G-Brownian motion; Strong Markov property
• ISSN: 0304-4149; 1879-209X
• DOI: 10.1016/j.spa.2020.09.015

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 τ and G-Brownian motion B, the reflection principle for B holds and (Bτ+t−Bτ)t≥0 is still a G-Brownian motion.