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• W2916627666 abstract "Consider the fractional Brownian Motion (fBM) $B^H={B^H(t): t in [0,1] }$ with Hurst index $Hin (0,1)$. We construct a probability space supporting both $B^H$ and a fully simulatable process $hat B_{epsilon}^H $ such that $$sup_{tin [0,1]}|B^H(t)-hat B_{epsilon}^H(t)| le epsilon$$ 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 extend our algorithm to the simulation of fBM driven stochastic differential equations $Y={Y(t):t in[0,1]}$. Under mild regularity conditions on the drift and diffusion coefficients of $Y$, we construct a probability space supporting both $Y$ and a fully simulatable process $hat Y_{epsilon}$ such that $$sup_{tin [0,1]}|Y(t)-hat Y_{epsilon}^H(t)| le epsilon$$ with probability one. Our algorithms enjoy the tolerance-enforcement feature, i.e., the error bounds can be updated sequentially. Thus, the algorithms can be readily combined with other simulation techniques like multilevel Monte Carlo to estimate expectation of functionals of fBMs efficiently." @default.
• W2916627666 created "2019-03-02" @default.
• W2916627666 creator A5028323106 @default.
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• W2916627666 date "2019-02-21" @default.
• W2916627666 modified "2023-09-26" @default.
• W2916627666 title "$epsilon$-Strong Simulation of Fractional Brownian Motion and Related Stochastic Differential Equations" @default.
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• W2916627666 hasPublicationYear "2019" @default.
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