### Abstract

The large deviation principle on phase space is proved for a class of Markov processes known as random population dynamics with catastrophes. In the paper we study the process which corresponds to the random population dynamics with linear growth and uniform catastrophes, where an eliminating portion of the population is chosen uniformly. The large deviation result provides an optimal trajectory of large fluctuation: it shows how the large fluctuations occur for this class of processes.

Original language | English |
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Pages (from-to) | 29-37 |

Number of pages | 9 |

Journal | Statistics and Probability Letters |

Volume | 149 |

DOIs | |

Publication status | Published - 1 Jun 2019 |

### Keywords

- Catastrophes
- Large deviation principle
- Local large deviation principle
- Population models

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## Cite this

Logachov, A., Logachova, O., & Yambartsev, A. (2019). Large deviations in a population dynamics with catastrophes.

*Statistics and Probability Letters*,*149*, 29-37. https://doi.org/10.1016/j.spl.2019.01.029