# Occupation Times on the Legs of a Diffusion Spider

## TL;DR

This paper extends the study of occupation times on a diffusion spider by providing a recursive formula for their joint moments.

## Contribution

The paper introduces a recursive formula for the Laplace transform of joint occupation times on a diffusion spider.

## Key findings

- A recursive formula for the Laplace transform of joint moments is derived.
- The approach provides an explicit formula for the joint moments of a Bessel spider.

## 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.