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1 results

  • Large deviation estimates of the crossing probability for pinned Gaussian processes

  • Part of
  • Lucia Caramellino, Barbara Pacchiarotti
  • Journal:
    Advances in Applied Probability / Volume 40 / Issue 2 / June 2008
    Published online by Cambridge University Press:
    01 July 2016, pp. 424-453
    Print publication:
    June 2008
    • Article
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  • The paper deals with the asymptotic behavior of the bridge of a Gaussian process conditioned to stay in n fixed points at n fixed past instants. In particular, functional large deviation results are stated for small time. Several examples are considered: integrated or not fractional Brownian motions and m-fold integrated Brownian motion. As an application, the asymptotic behavior of the exit probability is studied and used for the practical purpose of the numerical computation, via Monte Carlo methods, of the hitting probability up to a given time of the unpinned process.