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)


08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science

UniBE Contributor:

Molchanov, Ilya


500 Science > 510 Mathematics




Applied Probability Trust




Ilya Molchanov

Date Deposited:

09 Aug 2016 07:39

Last Modified:

09 Aug 2016 07:39


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