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Markov property of monotone L\'evy processes

Uwe Franz·Naofumi Muraki
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Abstract

Monotone L\'evy processes with additive increments are defined and studied. It is shown that these processes have a natural Markov structure and their Markov transition semigroups are characterized using the monotone L\'evy-Khintchine formula. Monotone L\'evy processes turn out to be related to classical L\'evy processes via Attal's ``remarkable transformation.'' A monotone analogue of the family of exponential martingales associated to a classical L\'evy process is also defined.

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BibTeXRIS

Uwe Franz, Naofumi Muraki. 2004-01-28. Markov property of monotone L\'evy processes. https://doi.org/10.1142/9789812701503_0003

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