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

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: |
09 Aug 2016 07:39 |

## URI: |
https://boris.unibe.ch/id/eprint/85369 |