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

## TL;DR

This paper calculates the frequency at which the density of a Lebesgue measure image, under a Brownian stochastic flow, crosses levels, and analyzes its behavior as levels grow large.

## Contribution

It provides a novel computation of level-crossing intensity for a specific stochastic flow and explores its asymptotic properties.

## Key findings

- Derived explicit formulas for level-crossing intensity.
- Analyzed asymptotic behavior as level height increases.
- Extended understanding of stochastic flow density properties.

## 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.