Anomalous scaling of dynamical large deviations of stationary Gaussian processes.

Abstract

Employing the optimal fluctuation method, we study the large deviation function of long-time averages (1/T)∫_{-T/2}^{T/2}x^{n}(t)dt,n=1,2,⋯, of centered stationary Gaussian processes. These processes are correlated and, in general, non-Markovian. We show that the anomalous scaling with time of the large-deviation function, recently observed for n>2 for the particular case of the Ornstein-Uhlenbeck process, holds for a whole class of stationary Gaussian processes.