Integrated Brownian motions and exact L2-small balls

• F. Gao ^[1] ; J. Hannig ^[2] ; F. Torcaso ^[3]
  1. [1] University of Idaho

     University of Idaho

     Estados Unidos

     
  2. [2] Colorado State University

     Colorado State University

     Estados Unidos

     
  3. [3] Johns Hopkins University

     Johns Hopkins University

     Estados Unidos

     

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• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 31, Nº. 3, 2003, págs. 1320-1337
• Idioma: inglés
• DOI: 10.1214/aop/1055425782
• Texto completo no disponible (Saber más ...)
• Resumen

  • We will introduce a class of m-times integrated Brownian motions. The exact asymptotic expansions for the L2-small ball probabilities will be discussed for members of this class, of which the usual m-times integrated Brownian motion is an example. Another example will be what we call an Euler-integrated Brownian motion. We will also find very sharp estimates for the asymptotics of the eigenvalues of the covariance operator of integrated Brownian motions and will, therefore, obtain exact, not just logarithmic, asymptotics.