On 1-point densities for Arratia flows with drift

TL;DR

This paper proves that the 1-point densities of Arratia flows with varying drift coefficients converge to the density of the flow with the limiting drift, under certain convergence conditions.

Contribution

It establishes the convergence of 1-point densities for Arratia flows with drift coefficients converging in L1 or L-infinity norms.

Findings

1-point densities converge under L1 or L-infinity drift convergence

Results apply to Arratia flows with drift

Provides a rigorous foundation for density convergence in stochastic flows

Abstract

We show that if drift coefficients of Arratia flows converge in $L_1(R)$ or $L_{\infty}(R)$ then the 1-point densities associated with these flows converge to the density for the flow with the limit drift.