Large-Deviation Functions for Nonlinear Functionals of a Gaussian Stationary Markov Process

Satya N. Majumdar; Alan J. Bray

doi:10.1103/physreve.65.051112

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Large-Deviation Functions for Nonlinear Functionals of a Gaussian Stationary Markov Process

Satya N. Majumdar·Alan J. Bray

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Abstract

We introduce a general method, based on a mapping onto quantum mechanics, for investigating the large-T limit of the distribution P(r,T) of the nonlinear functional r[V] = (1/T)\int_0^T dT' V[X(T')], where V(X) is an arbitrary function of the stationary Gaussian Markov process X(T). For T tending to infinity at fixed r we find that P(r,T) behaves as exp[-theta(r) T], where theta(r) is a large deviation function. We present explicit results for a number of special cases, including the case V(X) = X θ(X) which is related to the cooling and the heating degree days relevant to weather derivatives.

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Satya N. Majumdar, Alan J. Bray. 2004-06-11. Large-Deviation Functions for Nonlinear Functionals of a Gaussian Stationary Markov Process. https://doi.org/10.1103/physreve.65.051112

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