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Tail probabilities for non-standard risk and queueing processes with subexponential jumps. (English) Zbl 0942.60033
A known result involving the distribution tail of the maximum of a random walk with heavy tailed increments is extended and its validity is proved for more general stochastic processes. The exposition is completed by examples and counterexamples, among which some including superimposed renewal processes, Markovian arrival processes, semi-Markov input and Cox processes with piecewise constant intensities.

60G70 Extreme value theory; extremal stochastic processes
60G50 Sums of independent random variables; random walks
60K25 Queueing theory (aspects of probability theory)
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