arXiv subjects

B. Pacchiarotti

Publications and source records attributed to B. Pacchiarotti.

3 recordsLinked to original sources

arXiv2022

Large deviations for perturbed Gaussian processes and logarithmic asymptotic estimates for some exit probabilities

The main results in this paper concern large deviations for families of non-Gaussian processes obtained as suitable perturbations of continuous centered multivariate Gaussian processes which satisfy a large deviation principle. We present some corollaries and, as a consequence, we obtain logarithmic asymptotic estimates for exit probabilities from suitable halfspaces and quadrants.

math.PR↗

arXiv2020

Pathwise asymptotics for Volterra type stochastic volatility models

We study stochastic volatility models in which the volatility process is a positive continuous function of a continuous Volterra stochastic process. We state some pathwise large deviation principles for the scaled log-price.

math.PR↗

arXiv2007

Large deviation estimates of the crossing probability for pinned Gaussian processes

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 motion, $m$-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.

math.PR↗