Multiplicative white noise functionals and the Krylov-Veretennikov expansion for coalescing stochastic flows

TL;DR

This paper extends the Krylov-Veretennikov expansion to multiplicative white noise functionals and applies it to coalescing stochastic flows, including the Arratia flow, providing new analytical tools for these stochastic systems.

Contribution

It introduces a generalized Krylov-Veretennikov expansion for multiplicative white noise functionals and derives an analog for the Arratia coalescing flow.

Findings

Generalization of the Krylov-Veretennikov expansion for stochastic flows.

Derivation of an analog expansion for the Arratia flow.

Enhanced analytical framework for coalescing stochastic flows.

Abstract

In this article we consider multiplicative operator-valued white noise functionals related to a stochastic flow. A generalization of the Krylov-Veretennikov expansion is presented. An analog of such expansion for the Arratia flow is derived.