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- W3200370603 abstract "We study fast / slow systems driven by a fractional Brownian motion $B$ with Hurst parameter $Hin (frac 13, 1]$. Surprisingly, the slow dynamic converges on suitable timescales to a limiting Markov process and we describe its generator. More precisely, if $Y^varepsilon$ denotes a Markov process with sufficiently good mixing properties evolving on a fast timescale $varepsilon ll 1$, the solutions of the equation $$ dX^varepsilon = varepsilon^{frac 12-H} F(X^varepsilon,Y^varepsilon),dB+F_0(X^varepsilon,Y^varepsilon),dt; $$ converge to a regular diffusion without having to assume that $F$ averages to $0$, provided that $H< frac 12$. For $H > frac 12$, a similar result holds, but this time it does require $F$ to average to $0$. We also prove that the $n$-point motions converge to those of a Kunita type SDE. One nice interpretation of this result is that it provides a continuous interpolation between the homogenisation theorem for random ODEs with rapidly oscillating right-hand sides ($H=1$) and the averaging of diffusion processes ($H= frac 12$)." @default.
- W3200370603 created "2021-09-27" @default.
- W3200370603 creator A5016315238 @default.
- W3200370603 creator A5024301463 @default.
- W3200370603 date "2022-08-01" @default.
- W3200370603 modified "2023-09-26" @default.
- W3200370603 title "Generating Diffusions with Fractional Brownian Motion" @default.
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- W3200370603 doi "https://doi.org/10.1007/s00220-022-04462-2" @default.
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