Wong-Zakai Approximation for SDEs Driven by $G-$Brownian Motion

Abstract

In this paper, we build the equivalence between rough differential equations driven by the lifted $G$-Brownian motion and the corresponding Stratonovich type SDE through the Wong-Zakai approximation. The quasi-surely convergence rate of Wong-Zakai approximation to $G-$SDEs with mesh-size $\frac{1}{n}$ in the $\alpha$-Hölder norm is estimated as $(\frac{1}{n}{)}^{\frac{1}{2}-}.$ As corollary, we obtain the quasi-surely continuity of the above RDEs with respect to uniform norm.

arXiv admin note: substantial text overlap with arXiv:1510.01851

References in corpus (2)

• Smooth approximation of stochastic differential equations
• Optimal Unbiased Estimation for Maximal Distribution