The level-crossing intensity for the density of the image of the Lebesgue measure under the action of a Brownian stochastic flow

Abstract

In this paper we compute the level-crossing intensity for the density of the image of the Lebesgue measure under the action of a Brownian stochastic flow which is a smooth approximation of the Arratia flow and determine its asymptotic behaviour as the height of the level tends to infinity.