Critical growth of a semi-linear process

Molchanov, Ilya; Shcherbakov, Vadim; Zuyev, Sergei (2004). Critical growth of a semi-linear process. Journal of Applied Probability, 41(2), pp. 355-367. Applied Probability Trust

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This paper is motivated by the modelling of leaching of bacteria through soil. A semi-linear process X t − may be used to describe the soil-drying process between rain showers. This is a backward recurrence time process that corresponds to the renewal process of instances of rain. If a bacterium moves according to another process h, then the fact that h(t) stays above X t − means that the bacterium never hits a dry patch of soil and so survives. We describe a critical behaviour of h that separates the cases when survival is possible with a positive probability from the cases when this probability vanishes. An explicit formula for the survival probability is obtained in case h is linear and rain showers follow a Poisson process.

Item Type:	Journal Article (Original Article)
Division/Institute:	08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science
UniBE Contributor:	Molchanov, Ilya
Subjects:	500 Science > 510 Mathematics
ISSN:	1475-6072
Publisher:	Applied Probability Trust
Language:	English
Submitter:	Ilya Molchanov
Date Deposited:	09 Aug 2016 07:39
Last Modified:	05 Dec 2022 14:57
URI:	https://boris.unibe.ch/id/eprint/85369