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- W2620139928 abstract "Motivated by the modeling of the temporal structure of the velocity field in a highly turbulent flow, we propose and study a linear stochastic differential equation that involves the ingredients of an Ornstein-Uhlenbeck process, supplemented by a fractional Gaussian noise, of parameter $H$, regularized over a (small) time scale $ensuremath{epsilon}>0$. A peculiar correlation between these two plays a key role in the establishment of the statistical properties of its solution. We show that this solution reaches a stationary regime, which marginals, including variance and increment variance, remain bounded when $ensuremath{epsilon}ensuremath{rightarrow}0$. In particular, in this limit, for any $Hensuremath{in}]0,1[$, we show that the increment variance behaves at small scales as the one of a fractional Brownian motion of same parameter $H$. From the theoretical side, this approach appears especially well suited to deal with the (very) rough case $H<1/2$, including the boundary value $H=0$, and to design simple and efficient numerical simulations." @default.
- W2620139928 created "2017-06-05" @default.
- W2620139928 creator A5063393565 @default.
- W2620139928 date "2017-09-25" @default.
- W2620139928 modified "2023-10-13" @default.
- W2620139928 title "Regularized fractional Ornstein-Uhlenbeck processes and their relevance to the modeling of fluid turbulence" @default.
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- W2620139928 doi "https://doi.org/10.1103/physreve.96.033111" @default.
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