Integrability properties and limit theorems for the exit time from a cone of planar Brownian motion

TL;DR

This paper investigates the mathematical properties and limit behaviors of the time it takes for a planar Brownian motion to exit a cone, using integrability analysis and Bougerol's identity for validation.

Contribution

It provides new integrability results and limit theorems specifically for the exit time of planar Brownian motion from a cone, with verification through Bougerol's identity.

Findings

Derived integrability properties of exit times

Established limit theorems for exit times

Validated results using Bougerol's identity

Abstract

We obtain some integrability properties and some limit theorems for the exit time from a cone of a planar Brownian motion, and we check that our computations are correct via Bougerol's identity.