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arXiv · 1511.00206

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

Shige Peng·Huilin Zhang
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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 $α$-Hölder 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.

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Shige Peng, Huilin Zhang. 2020-11-10. Wong-Zakai Approximation for SDEs Driven by $G-$Brownian Motion. https://arxiv.org/abs/1511.00206

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