Stationary Distributions for Two-Dimensional Sticky Brownian Motions: Exact Tail Asymptotics and Extreme Value Distributions

2018/06/12 by Hongshuai Dai, Dai, Hongshuai, Yiqiang Q. Zhao +1
Business, Management and Accounting · Economics, Econometrics and Finance · Mathematics · #60J10 #60K25 #Advanced Queuing Theory Analysis #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1806.04660

openalex publication_date 2018/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider a two-dimensional sticky Brownian motion. Sticky Brownian motions can be viewed as time-changed semimartingale reflecting Brownian motions, which find applications in many areas including queueing theory and mathematical finance. For example, a sticky Brownian motion can be used to model a storage system.with exceptional services. In this paper, we focus on stationary distributions for sticky Brownian motions. The main results obtained here include tail asymptotic properties in boundary stationary distributions, marginal distributions, and joint distributions. The kernel method, copula concept and extreme value theory are main tools used in our analysis.

Citations

• Stochastic Calculus for a Time-Changed Semimartingale and the Associated Stochastic Differential Equations
• A Kernel Method for Exact Tail Asymptotics --- Random Walks in the Quarter Plane
• The Parabolic Differential Equations and the Associated Semi-Groups of Transformations

Related

• Multidimensional Sticky Brownian Motions: Tail Behaviour of the Joint Stationary Distribution
• Trivariate distribution of sticky Brownian motion
• Slowing time: Markov-modulated Brownian motion with a sticky boundary
• Exact tail asymptotics for a three dimensional Brownian-driven tandem queue with intermediate inputs
• Strong convergence to two-dimensional alternating Brownian motion processes