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Wong-Zakai Approximation for SDEs Driven by $G-$Brownian Motion (1511.00206v4)
Published 1 Nov 2015 in math.PR
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 $\alpha$-H\"older norm is estimated as $(\frac{1}{n}){\frac12-}.$ As corollary, we obtain the quasi-surely continuity of the above RDEs with respect to uniform norm.