The cocycle property of stochastic differential equations driven by G-Brownian motion

Abstract

In this paper, solutions of the following non-Lipschitz stochastic differential equations driven by G-Brownian motion: X_t = x + \int_0^t {b(s,\omega ,X_s )ds} + \int_0^t {h(s,\omega ,X_s )d\left\langle B \right\rangle _s } + \int_0^t {\sigma (s,\omega ,X_s )dB_s } are constructed. It is shown that they have the cocycle property. Moreover, under some special non-Lipschitz conditions, they are bi-continuous with respect to t, x.

Keywords

Cocycle property / Non-Lipschitz condition / SDEs driven by G-Brownian motion

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