It\^o-Wiener expansion for functionals of the Arratia's flow $n$-point motion

TL;DR

This paper develops an Itô-Wiener expansion for square integrable functionals of the Arratia flow's n-point motion, providing a new stochastic integral construction using change of measure techniques.

Contribution

It introduces a novel Itô-Wiener expansion for Arratia flow functionals and a new multiple stochastic integral construction along flow trajectories.

Findings

Established an Itô-Wiener expansion for Arratia flow functionals

Developed a new method for constructing multiple stochastic integrals

Enhanced understanding of the structure of flow-dependent functionals

Abstract

The structure of square integrable functionals measurable with respect to the $n-$point motion of the Arratia flow is studied. Relying on the change of measure technique, a new construction of multiple stochastic integrals along trajectories of the flow is presented. The analogue of the It\^o-Wiener expansion for square integrable functionals from the Arratia's flow $n-$point motion is constructed.