Multidimensional Sticky Brownian Motions: Tail Behaviour of the Joint Stationary Distribution

TL;DR

This paper investigates the tail behavior and large deviations of the joint stationary distribution of multidimensional sticky Brownian motions, which are relevant in fields like queuing theory and finance, focusing on their stability and probabilistic properties.

Contribution

It provides a detailed analysis of the tail behavior and large deviations principles for the stationary distribution of multidimensional sticky Brownian motions, a topic not extensively explored before.

Findings

Established the large deviations principle for the stationary distribution.

Characterized the tail asymptotics of the joint stationary distribution.

Demonstrated applications in queuing systems and financial models.

Abstract

Sticky Brownian motions, as time-changed semimartingale reflecting Brownian motions, have various applications in many fields, including queuing theory and mathematical finance. In this paper, we are concerned about the stationary distributions of a multidimensional sticky Brownian motion, provided it is stable. We will study the large deviations principle for stationary distribution and the tail behaviour of the joint stationary distribution.