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Large Deviation Approaches for the Numerical Computation of the Hitting Probability for Gaussian Processes

Author

Listed:
  • Lucia Caramellino

    (Università di Roma Tor Vergata)

  • Barbara Pacchiarotti

    (Università di Roma Tor Vergata)

  • Simone Salvadei

    (Università di Roma Tor Vergata, SEFEMEQ)

Abstract

We state large deviations for small time of a pinned n-conditional Gaussian process, i.e. the bridge of a Gaussian process conditioned to stay in n fixed points at n fixed past instants, by letting all the past monitoring instants to depend on the small parameter going to 0. Differently from what already developed in Caramellino and Pacchiarotti (Adv Appl Probab 40:424–453, 2008), this procedure is able to catch the dependence on the past observations. We apply the results to numerical experiments that involve the fractional Brownian motion, for the computation of the hitting probability through Monte Carlo methods.

Suggested Citation

  • Lucia Caramellino & Barbara Pacchiarotti & Simone Salvadei, 2015. "Large Deviation Approaches for the Numerical Computation of the Hitting Probability for Gaussian Processes," Methodology and Computing in Applied Probability, Springer, vol. 17(2), pages 383-401, June.
    • Handle: RePEc:spr:metcap:v:17:y:2015:i:2:d:10.1007_s11009-013-9364-5
    DOI: 10.1007/s11009-013-9364-5
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    References listed on IDEAS

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    1. Gobet, Emmanuel, 2000. "Weak approximation of killed diffusion using Euler schemes," Stochastic Processes and their Applications, Elsevier, vol. 87(2), pages 167-197, June.
    2. Gobet, Emmanuel & Menozzi, Stéphane, 2004. "Exact approximation rate of killed hypoelliptic diffusions using the discrete Euler scheme," Stochastic Processes and their Applications, Elsevier, vol. 112(2), pages 201-223, August.
    3. Mandjes, Michel & Mannersalo, Petteri & Norros, Ilkka & van Uitert, Miranda, 2006. "Large deviations of infinite intersections of events in Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 116(9), pages 1269-1293, September.
    4. Paolo Baldi & Lucia Caramellino & Maria Gabriella Iovino, 1999. "Pricing General Barrier Options: A Numerical Approach Using Sharp Large Deviations," Mathematical Finance, Wiley Blackwell, vol. 9(4), pages 293-321, October.
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    Cited by:

    1. Miriana Cellupica & Barbara Pacchiarotti, 2021. "Pathwise Asymptotics for Volterra Type Stochastic Volatility Models," Journal of Theoretical Probability, Springer, vol. 34(2), pages 682-727, June.

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