Occupation times on the legs of a diffusion spider

TL;DR

This paper derives recursive and explicit formulas for the joint moments of occupation times on the legs of a diffusion spider, extending previous results for one-dimensional diffusions and including the Brownian spider as a special case.

Contribution

It introduces a recursive formula for the Laplace transform of joint moments on diffusion spiders and provides explicit formulas for Bessel spiders, advancing the understanding of occupation times.

Findings

Recursive formula for Laplace transform of joint moments

Explicit formulas for Bessel spiders' occupation times

Extension of one-dimensional diffusion results

Abstract

We study the joint moments of occupation times on the legs of a diffusion spider. Specifically, we give a recursive formula for the Laplace transform of the joint moments, which extends earlier results for a one-dimensional diffusion. For a Bessel spider, of which the Brownian spider is a special case, our approach yields an explicit formula for the joint moments of the occupation times.