Large deviation approaches for the numerical computation of the hitting probability for Gaussian processes

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 Pacchiarott