Kac–Lévy Processes

Nikita Ratanov

doi:10.1007/s10959-018-0873-6

Kac–Lévy Processes

Nikita Ratanov

Producción científica: Contribución a una revista › Artículo de Investigación › revisión exhaustiva

6 Citas (Scopus)

Resumen

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.

Idioma original	Inglés estadounidense
Páginas (desde-hasta)	239-267
Número de páginas	29
Publicación	Journal of Theoretical Probability
Volumen	33
N.º	1
DOI	https://doi.org/10.1007/s10959-018-0873-6
Estado	Publicada - mar. 1 2020

Áreas temáticas de ASJC Scopus

Estadística y probabilidad
Matemáticas General
Estadística, probabilidad e incerteza

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10.1007/s10959-018-0873-6

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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

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