Critical growth of a semi-linear process

Molchanov, I., Shcherbakov, V. and Zuyev, S. (2004) Critical growth of a semi-linear process. Journal of Applied Probability, 41, pp. 355-367.

Abstract

This paper is motivated by the modelling of leaching of bacteria through soil. A semi-linear process Xt- 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 Xt- 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: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: UNSPECIFIED
• Authors: Molchanov, I., Shcherbakov, V., and Zuyev, S.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Statistics
• Journal Name: Journal of Applied Probability