Title:
Modeling some aspects of the random nature of fluid turbulence and of multifractality using fractional Ornstein-Uhlenbeck processes.
Abstract:
Mostly motivated by the modeling of velocity fluctuations in fully developed turbulent flows, I define and study a linear stochastic differential equation (SDE) which unique solution reaches a stationary regime and is of finite variance. The underlying non Markovian dynamics is governed by a fractional Gaussian noise, necessarily regularized over a small parameter in order to have a proper meaning. We show that its solution becomes Holder continuous, characterized by the parameter 0