Stochastic flows: Dispersion of a mass distribution and Lagrangian observations of a random field.

摘要

e consider two classical problems from statistical fluid mechanics in the modern probabilistic setting of stochastic flows based on stochastic differential equations. Such flows model spatially coherent "noise" superimposed on classical velocity fields. Their theory was developed over the past fifteen years by Kunita, Harris, Baxendale, and Le Jan, among others.;The first problem we treat is the dispersion of a mass distribution carried by an isotropic Brownian flow ;The second problem we consider concerns Lagrangian observations of a random field A made by a particle carried by a general stochastic flow F. Assuming that A and F are homogeneous, we obtain a formula for the distribution of the Lagrangian observation