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Lévy processes conditioned on having a large height process

Mathieu Richard (2013)

Annales de l'I.H.P. Probabilités et statistiques

In the present work, we consider spectrally positive Lévy processes ( X t , t ≥ 0 ) not drifting to + ∞ and we are interested in conditioning these processes to reach arbitrarily large heights (in the sense of the height process associated with X ) before hitting 0 . This way we obtain a new conditioning of Lévy processes to stay positive. The (honest) law ℙ x ☆ of this conditioned process (starting at x g t ; 0 ) is defined as a Doob h -transform via a martingale. For Lévy processes with infinite variation paths, this martingale...

Limited space double channel Markovian queue with heterogeneus servers.

O.P. Sharma, J. Dass (1990)

Trabajos de Investigación Operativa

For a double channel Markovian queue with finite waiting space and unequal service rates at the two counters, the difference equations satisfied by the Laplace transforms of the state probabilities at finite time are solved and the state probabilities have been obtained. The closed form of the state probabilities can be used to obtain the important parameters of the system.

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