Stochastic differential equations driven by fractional Brownian motion and application to fluids.

摘要

Stochastic differential equations find applications in diverse disciplines. Some applications, such as turbulence theory, require sophisticated models which take into account the effect of statistical properties of the solution of the turbulent fluid flow. These models are driven by a fractional Brownian motion (FBM).;In this thesis, we study the equation of a vortex filament and prove its wellposedness. This is an integrodifferential equation driven by FBM with Hurst parameter H > 1=2. We use a pathwise argument to define the stochastic integral using the Holder continuity property of the FBM.