caa a22 4500 605519978 CHVBK 20210128100733.0 cr unu---uuuuu 210128e20150601xx s 000 0 eng 10.1007/s11009-013-9364-5 doi (NATIONALLICENCE)springer-10.1007/s11009-013-9364-5 Large Deviation Approaches for the Numerical Computation of the Hitting Probability for Gaussian Processes [Elektronische Daten] [Lucia Caramellino, Barbara Pacchiarotti, Simone Salvadei] 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. Springer Science+Business Media New York, 2013 Conditioned Gaussian processes nationallicence Reproducing kernel Hilbert spaces nationallicence Large deviations nationallicence Exit time probabilities nationallicence Monte Carlo methods nationallicence Caramellino Lucia Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca, Scientifica 1, 00133, Roma, Italy aut Pacchiarotti Barbara Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca, Scientifica 1, 00133, Roma, Italy aut Salvadei Simone Università di Roma Tor Vergata, SEFEMEQ, Via Columbia 2, 00133, Roma, Italy aut Methodology and Computing in Applied Probability Springer US; http://www.springer-ny.com 17/2(2015-06-01), 383-401 1387-5841 17:2<383 2015 17 11009 https://doi.org/10.1007/s11009-013-9364-5 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s11009-013-9364-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Caramellino Lucia Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca, Scientifica 1, 00133, Roma, Italy aut NATIONALLICENCE 700 1- Pacchiarotti Barbara Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca, Scientifica 1, 00133, Roma, Italy aut NATIONALLICENCE 700 1- Salvadei Simone Università di Roma Tor Vergata, SEFEMEQ, Via Columbia 2, 00133, Roma, Italy aut NATIONALLICENCE 773 0- Methodology and Computing in Applied Probability Springer US; http://www.springer-ny.com 17/2(2015-06-01), 383-401 1387-5841 17:2<383 2015 17 11009