Large deviations for functionals of some self-similar Gaussian processes
Large deviations for functionals of some self-similar Gaussian processes
We prove large deviation principles for ∫0tγ(Xs)ds, where X is a d-dimensional self-similar Gaussian process and γ(x) takes the form of the Dirac delta function δ(x), |x|−β with β∈(0,d), or ∏i=1d|xi|−βi with βi∈(0,1). In particular, large deviations are obtained for the functionals of d-dimensional fractional Brownian motion, sub-fractional Brownian motion …