Lower tail probabilities for Gaussian processes

• Wenbo V. Li ^[1] ; Qi-Man Shao ^[2]
  1. [1] University of Delaware

     University of Delaware

     Estados Unidos

     
  2. [2] University of Oregon
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 32, Nº. 1, 1, 2004, págs. 216-242
• Idioma: inglés
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• Resumen

  • Let X=(Xt)t∈S be a real-valued Gaussian random process indexed by S with mean zero. General upper and lower estimates are given for the lower tail probability P(supt∈S(Xt−Xt0)≤x) as x→0, with t0∈S fixed. In particular, sharp rates are given for fractional Brownian sheet. Furthermore, connections between lower tail probabilities for Gaussian processes with stationary increments and level crossing probabilities for stationary Gaussian processes are studied. Our methods also provide useful information on a random pursuit problem for fractional Brownian particles.