Random motion with gamma-distributed alternating velocities in biological modeling

Authors:
Antonio Di Crescenzo;Barbara Martinucci
Affiliations:
Dipartimento di Matematica e Informatica, Università di Salerno, Fisciano, SA, Italy;Dipartimento di Matematica e Informatica, Università di Salerno, Fisciano, SA, Italy
Venue:
EUROCAST'07 Proceedings of the 11th international conference on Computer aided systems theory
Year:
2007

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Abstract

Motivated by applications in mathematical biology concerning randomly alternatingmotion ofmicro-organisms, we analyze a generalized integrated telegraph process. The random times between consecutive velocity reversals are gamma-distributed, and perform an alternating renewal process. We obtain the probability law and the mean of the process.