Theory of Probability and Mathematical Statistics
Large deviations for perturbed Gaussian processes and logarithmic asymptotic estimates for some exit probabilities
Claudio Macci and Barbara Pacchiarotti
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Abstract: 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.
Keywords: Lagrange multipliers method, most likely path leading to exit, reproducing kernel Hilbert space, supermodular order
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