# $\epsilon$-Strong Simulation of Fractional Brownian Motion and Related Stochastic Differential Equations

@article{Chen2019epsilonStrongSO, title={\$\epsilon\$-Strong Simulation of Fractional Brownian Motion and Related Stochastic Differential Equations}, author={Yi Chen and Jing Dong and Hao Ni}, journal={arXiv: Probability}, year={2019} }

Consider the fractional Brownian Motion (fBM) $B^H=\{B^H(t): t \in [0,1] \}$ with Hurst index $H\in (0,1)$. We construct a probability space supporting both $B^H$ and a fully simulatable process $\hat B_{\epsilon}^H $ such that $$\sup_{t\in [0,1]}|B^H(t)-\hat B_{\epsilon}^H(t)| \le \epsilon$$ with probability one for any user specified error parameter $\epsilon>0$. When $H>1/2$, we further enhance our error guarantee to the $\alpha$-Holder norm for any $\alpha \in (1/2,H)$. This enables us to…

## One Citation

### $\varepsilon $-strong simulation of the convex minorants of stable processes and meanders

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Using marked Dirichlet processes we characterise the law of the convex minorant of the meander for a certain class of L\'evy processes, which includes subordinated stable and symmetric L\'evy…

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