### Abstract

We consider a class of Gaussian processes which are obtained as height processes of some (d + 1)-dimensional dynamic random interface model on ℤ<sup>d</sup>. We give an estimate of persistence probability, namely, large T asymptotics of the probability that the process does not exceed a fixed level up to time T. The interaction of the model affects the persistence probability and its asymptotics changes depending on the dimension d.

Original language | English |
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Pages (from-to) | 146-163 |

Number of pages | 18 |

Journal | Advances in Applied Probability |

Volume | 47 |

Issue number | 1 |

Publication status | Published - 2015 Mar 1 |

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### Keywords

- Gaussian process
- Interacting diffusion process
- Persistence probability
- Random interface

### ASJC Scopus subject areas

- Applied Mathematics
- Statistics and Probability