Persistence probability for a class of Gaussian processes related to random interface models

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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 languageEnglish
Pages (from-to)146-163
Number of pages18
JournalAdvances in Applied Probability
Volume47
Issue number1
Publication statusPublished - 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

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