Krylov-Veretennikov formula for functionals from the stopped Wiener process

TL;DR

This paper develops a Krylov-Veretennikov type formula for functionals of stopped Wiener processes, providing a new representation for measures absolutely continuous with respect to such processes and extending stochastic integral expansions.

Contribution

It introduces an analogue of the Krylov-Veretennikov formula for functionals of stopped Wiener processes, expanding stochastic calculus tools for these measures.

Findings

Derived multiple stochastic integrals for stopped Wiener processes

Established an analogue of the Krylov-Veretennikov formula for functionals

Extended Itô-Wiener expansions to new classes of measures

Abstract

We consider a class of measures absolutely continuous with respect to the distribution of the stopped Wiener process $w(\cdot\wedge\tau)$. Multiple stochastic integrals, that lead to the analogue of the It\^o-Wiener expansions for such measures, are described. An analogue of the Krylov-Veretennikov formula for functionals $f=\varphi(w(\tau))$ is obtained.