Clark formula for local time for one class of Gaussian processes

TL;DR

This paper develops a Clark formula for the local time of Gaussian integrators, providing multiple representations and analyzing the one with minimal L2-norm, advancing the understanding of stochastic local times.

Contribution

It introduces a chaotic decomposition and Clark formula analog for local time of Gaussian integrators, including multiple representations and minimal norm analysis.

Findings

Multiple Clark representations for local time are derived.

The representation with minimal L2-norm is identified.

The approach extends stochastic calculus for Gaussian integrators.

Abstract

In the article we present chaotic decomposition and analog of the Clark formula for the local time of Gaussian integrators. Since the integral with respect to Gaussian integrator is understood in Skorokhod sense, then there exist more than one Clark representation for the local time. We present different representations and discuss the representation with the minimal L_2-norm.