Clark representation for self-intersection local times of Gaussian integrators

TL;DR

This paper proves the existence of multiple self-intersection local times for Gaussian integrators, describes their Ito-Wiener expansion, and establishes Clark representation for a specific class of these integrators.

Contribution

It introduces the Clark representation for Gaussian integrators generated by operators with finite dimensional kernels, expanding understanding of their self-intersection local times.

Findings

Existence of multiple self-intersection local times proven.

Ito-Wiener expansion of these local times described.

Clark representation established for Gaussian integrators with finite dimensional kernels.

Abstract

In present article we prove the existence of multiple self-intersection local times, describe its Ito-Wiener expansion and establish Clark representation for the class of Gaussian integrators generated by operators with a finite dimensional kernel.