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

Lucia Caramellino, Barbara Pacchiarotti () and Simone Salvadei
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Lucia Caramellino: Università di Roma Tor Vergata
Barbara Pacchiarotti: Università di Roma Tor Vergata
Simone Salvadei: Università di Roma Tor Vergata, SEFEMEQ

Methodology and Computing in Applied Probability, 2015, vol. 17, issue 2, 383-401

Abstract: 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.

Keywords: Conditioned Gaussian processes; Reproducing kernel Hilbert spaces; Large deviations; Exit time probabilities; Monte Carlo methods; 60F10; 60G15; 65C05 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11009-013-9364-5

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