Kac–Lévy Processes

Nikita Ratanov

doi:10.1007/s10959-018-0873-6

Kac–Lévy Processes

Nikita Ratanov

Research output: Contribution to journal › Research Article › peer-review

6 Scopus citations

Abstract

Markov-modulated Lévy processes with two different regimes of restarting are studied. These regimes correspond to the completely renewed process and to the process of Markov modulation, accompanied by jumps. We give explicit expressions for the Lévy–Khintchine exponent in the case of a two-state underlying Markov chain. For the renewal case, the limit distributions (as t→ ∞) are obtained. In the case of processes with jumps, we present some results for the exponential functional.

Original language	English (US)
Pages (from-to)	239-267
Number of pages	29
Journal	Journal of Theoretical Probability
Volume	33
Issue number	1
DOIs	https://doi.org/10.1007/s10959-018-0873-6
State	Published - Mar 1 2020

All Science Journal Classification (ASJC) codes

Statistics and Probability
General Mathematics
Statistics, Probability and Uncertainty

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abstract = "Markov-modulated L{\'e}vy processes with two different regimes of restarting are studied. These regimes correspond to the completely renewed process and to the process of Markov modulation, accompanied by jumps. We give explicit expressions for the L{\'e}vy–Khintchine exponent in the case of a two-state underlying Markov chain. For the renewal case, the limit distributions (as t→ ∞) are obtained. In the case of processes with jumps, we present some results for the exponential functional.",

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AB - Markov-modulated Lévy processes with two different regimes of restarting are studied. These regimes correspond to the completely renewed process and to the process of Markov modulation, accompanied by jumps. We give explicit expressions for the Lévy–Khintchine exponent in the case of a two-state underlying Markov chain. For the renewal case, the limit distributions (as t→ ∞) are obtained. In the case of processes with jumps, we present some results for the exponential functional.

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Kac–Lévy Processes

Abstract

All Science Journal Classification (ASJC) codes

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