71 citations · 210 across the 21 of their papers we have counts for
7 papers · 1 filter
Affine Point Processes: Refinements to Large-Time Asymptotics
Xuefeng Gao, Lingjiong Zhu
Affine point processes are a class of simple point processes with self- and mutually-exciting properties, and they have found useful applications in several areas. In this paper, w…
Functional central limit theorems for stationary Hawkes processes and application to infinite-server queues
Xuefeng Gao, Lingjiong Zhu
A univariate Hawkes process is a simple point process that is self-exciting and has clustering effect. The intensity of this point process is given by the sum of a baseline intensi…
Large deviations and applications for Markovian Hawkes processes with a large initial intensity
Xuefeng Gao, Lingjiong Zhu
Hawkes process is a class of simple point processes that is self-exciting and has clustering effect. The intensity of this point process depends on its entire past history. It has…
Limit theorems for Markovian Hawkes processes with a large initial intensity
Xuefeng Gao, Lingjiong Zhu
Hawkes process is a simple point process that is self-exciting and has clustering effect. The intensity of this point process depends on its entire past history. It has wide applic…
Validity of heavy-traffic steady-state approximations in many-server queues with abandonment
J. G. Dai, A. B. Dieker, Xuefeng Gao
We consider GI/Ph/n+M parallel-server systems with a renewal arrival process, a phase-type service time distribution, n homogenous servers, and an exponential patience time distrib…
Positive recurrence of piecewise Ornstein-Uhlenbeck processes and common quadratic Lyapunov functions
A. B. Dieker, Xuefeng Gao
We study the positive recurrence of piecewise Ornstein-Uhlenbeck (OU) diffusion processes, which arise from many-server queueing systems with phase-type service requirements. These…
Sensitivity analysis for diffusion processes constrained to an orthant
A. B. Dieker, X. Gao
This paper studies diffusion processes constrained to the positive orthant under infinitesimal changes in the drift. Our first main result states that any constrained function and…