Representations of the finite-dimensional point densities in Arratia flows with drift

TL;DR

This paper derives new representations for finite-dimensional densities in Arratia flows with drift, using conditional expectations of stochastic exponentials related to Girsanov's theorem, advancing understanding of these stochastic processes.

Contribution

It introduces a novel representation of densities for Arratia flows with drift, connecting them to stochastic exponentials and Girsanov's theorem analogs.

Findings

Explicit formulas for finite-dimensional densities

Connections to Girsanov's theorem in Arratia flows

Enhanced understanding of point process distributions

Abstract

We derive representations for finite-dimensional densities of the point processed associated with an Arratia flow with drift in terms of conditional expectations of the stochastic exponentials appearing in the analog of the Girsanov theorem for Arratia flows.