Publication TypeJournal Article
Year of Publication2018
JournalNeural, Parallel, and Scientific Computations
Start Page119
Date Published2018
Keywords60G25, 60G50, 60G51, 60G52, 60G55, 60G57, 60K05, 60K35, 60K40, 90B10, 90B15, 90B18, 90B25

We study a class of monotone delayed marked point processes that model stochastic networks (under attacks), status of queueing systems during vacation modes, responses to cancer treatments (such as chemotherapy and radiation), hostile ambushes in economics and warfare. We are interested in the behavior of such a process about a fixed threshold. It presents an analytic challenge, because of the arbitrary nature of random marks. We target the first passage time, pre-first passage time, the status of the associated continuous time parameter process between these two epochs, and the status of the process upon these two epochs. A joint functional of these stochastic quantities is investigated in the transient mode. Analytically tractable formulas are obtained and demonstrated on special cases of marked Poisson processes.

Refereed DesignationRefereed
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