Anomalous scaling of dynamical large deviations of stationary Gaussian processes

Abstract

Employing the optimal fluctuation method (OFM), we study the large deviation function of long-time averages $(1/T){\int }_{-T/2}^{T/2}{x}^n(t)dt$, $n=1,2,\dots$, 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.

7 pages, 3 figures

References in corpus (2)

• The large deviation approach to statistical mechanics
• Large Deviations in Single File Diffusion

Cited by in corpus (19)

• Anomalous scaling and first-order dynamical phase transition in large deviations of the Ornstein-Uhlenbeck process
• Condensation transition in large deviations of self-similar Gaussian processes with stochastic resetting
• Giant leaps and long excursions: fluctuation mechanisms in systems with long-range memory
• Large deviations in chaotic systems: exact results and dynamical phase transition
• Geometrical optics of large deviations of fractional Brownian motion
• Noise correction of large deviations with anomalous scaling
• Path integrals for fractional Brownian motion and fractional Gaussian noise
• Generating stochastic trajectories with global dynamical constraints
• Anomalous scalings of fluctuations of the area swept by a Brownian particle trapped in a $|x|$ potential
• Occupation time of a system of Brownian particles on the line with steplike initial condition
• Geometrical optics of large deviations of Brownian motion in inhomogeneous media
• Rare Events and Single Big Jump Effects in Ornstein-Uhlenbeck Processes
• Dynamical large deviations of the fractional Ornstein-Uhlenbeck process
• Local time of an Ornstein-Uhlenbeck particle
• Data-driven analysis of annual rain distributions
• Subleading-order theory for condensation transitions in large deviations of sums of independent and identically distributed random variables
• Beyond the Big Jump: A Perturbative Approach to Stretched-Exponential Processes
• Short-time large deviations of first-passage functionals for high-order stochastic processes
• Dimensionality-induced dynamical phase transition in the large deviation of local time density for Brownian motion