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Passage times in fluid models with application to risk processes. (English) Zbl 1110.60067
The author derives a variety of passage time distributions in the canonical Markov modulated fluid flow model in terms of its busy period distribution and that of its reflection about the time axis. The use of these distributions is illustrated in the context of a general insurance risk model with Markovian arrival of claims and phase type distributed claim sizes. The paper leans heavily on results previously derived by S. Ahn and the author [Stoch. Models 20, No. 1, 71–101 (2004; Zbl 1038.60086); J. Appl. Probab. 42, No. 2, 531–549 (2005; Zbl 1085.60065); Stoch. Models 22, No. 1, 129–147 (2006)].

60J25 Continuous-time Markov processes on general state spaces
60K15 Markov renewal processes, semi-Markov processes
60K25 Queueing theory (aspects of probability theory)
60K37 Processes in random environments
Full Text: DOI
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