On the excursions of reflected local time processes and stochastic fluid queues

2010/06/10 by Takis Konstantopoulos, Konstantopoulos, Takis, Andreas E. Kyprianou +3
Mathematics · #60G10 #60G51 #90B15 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60G10 #msc:60G51 #msc:90B15

paper · pdf · doi:10.48550/arxiv.1006.2120

29 pages, 4 figures

arxiv created 2010/06/10 · arxiv updated 2010/06/11

Abstract

This paper extends previous work by the authors. We consider the local time process of a strong Markov process, add negative drift, and reflect it à la Skorokhod. The resulting process is used to model a fluid queue. We derive an expression for the joint law of the duration of an excursion, the maximum value of the process on it, and the time distance between successive excursions. We work with a properly constructed stationary version of the process. Examples are also given in the paper.

Related

• Analysis of stochastic fluid queues driven by local time processes
• Asymptotic behavior of local times of compound Poisson processes with drift in the infinite variance case
• Processes with inert drift
• Strong Approximations for Time-Dependent Queues
• Weak convergence of quasi-birth-and-death processes with rational arrival process components to fluid queues