On the strong Markov property for stochastic differential equations driven by [formula omitted]-Brownian motion

Abstract

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.