Abstract
For a class of birth and death processes under a heavy traffic condition, the asymptotic behavior of functionals of their jumps is investigated. It is shown that, under suitable normalization, the functionals converge in law to a process that is the sum of a Brownian motion and a constant times the local time of a reflecting Brownian motion at zero. Some applications to queueing processes are presented.
Citation
Keigo Yamada. Sung Jo Hong. "A Limit Theorem for Functionals of Jumps of Birth and Death Processes under Heavy Traffic Condition." Ann. Appl. Probab. 3 (3) 840 - 862, August, 1993. https://doi.org/10.1214/aoap/1177005367
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