Large deviations for functionals of some self-similar Gaussian processes

Abstract

ABSTRACT We prove large deviation principles for , where X is a d-dimensional self-similar Gaussian process and takes the form of the Dirac delta function , with , or with . In particular, large deviations are obtained for the functionals of d-dimensional fractional Brownian motion, sub-fractional Brownian motion and bi-fractional Brownian motion. As an application, the critical exponential integrability of the functionals is discussed.