Reflected Brownian motion in a wedge: sum-of-exponential stationary densities

TL;DR

This paper characterizes when the stationary density of reflected Brownian motion in a wedge can be expressed as a finite sum of exponential products, providing explicit formulas under these conditions.

Contribution

It establishes necessary and sufficient conditions for finite sum-of-exponential stationary densities and derives explicit formulas using geometric reflection principles.

Findings

Identifies conditions for finite sum-of-exponential densities

Provides explicit formulas for these densities

Enhances understanding of reflected Brownian motion in wedges

Abstract

We give necessary and sufficient conditions for the stationary density of semimartingale reflected Brownian motion in a wedge to be written as a finite sum of terms of exponential product form. Relying on geometric ideas reminiscent of the reflection principle, we give an explicit formula for the density in such cases.