Dynamical large deviations of linear diffusions

du, Buisson, Johan; Touchette, Hugo

doi:10.48550/arxiv.2212.12022

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“…Since this case is already much studied on its own independently of the Pearson family, with its supplementary specific properties as a Gaussian process, it will not be discussed in the present paper. Its large deviations properties have already been much studied even in higher dimensions where non-equilibrium steady states are possible (see the two recent papers [69,70], the PhD thesis [26], as well as the references therein).…”

Section: Bmentioning

confidence: 99%

Jump-drift and jump-diffusion processes: large deviations for the density, the current and the jump-flow and for the excursions between jumps

Monthus¹

2021

J. Stat. Mech.

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The Pearson family of ergodic diffusions with a quadratic diffusion coefficient and a linear force are characterized by explicit dynamics of their integer moments and by explicit relaxation spectral properties towards their steady state. Besides the Ornstein-Uhlenbeck process with a Gaussian steady state, the other representative examples of the Pearson family are the Square-Root or the Cox-Ingersoll-Ross process converging towards the Gamma-distribution, the Jacobi process converging towards the Beta-distribution, the reciprocal-Gamma process (corresponding to an exponential functional of the Brownian motion) that converges towards the Inverse-Gamma-distribution, the Fisher-Snedecor process, and the Student process, so that the last three steady states display heavytails. The goal of the present paper is to analyze the large deviations properties of these various diffusion processes in a unified framework. We first consider the Level 1 concerning time-averaged observables over a large time-window T : we write the first rescaled cumulants for generic observables and we identify the specific observables whose large deviations can be explicitly computed from the dominant eigenvalue of the appropriate deformed-generator. The explicit large deviations at Level 2 concerning the time-averaged density are then used to analyze the statistical inference of model parameters from data on a very long stochastic trajectory in order to obtain the explicit rate function for the two inferred parameters of the Pearson linear force.

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Section: Bmentioning

confidence: 99%

Jump-drift and jump-diffusion processes: large deviations for the density, the current and the jump-flow and for the excursions between jumps

Monthus¹

2021

J. Stat. Mech.

View full text Add to dashboard Cite

show abstract

Dynamical large deviations of linear diffusions

Cited by 1 publication

References 0 publications

Jump-drift and jump-diffusion processes: large deviations for the density, the current and the jump-flow and for the excursions between jumps

Jump-drift and jump-diffusion processes: large deviations for the density, the current and the jump-flow and for the excursions between jumps

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