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

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

2002-02-08

arxiv.org/abs/cond-mat/0202138v2

Phys. Rev. E 65, 051112 (2002)

Physics

Condensed Matter

Statistical Mechanics

8 pages

Scientific paper

10.1103/PhysRevE.65.051112

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 \theta(X) which is related to the cooling and the heating degree days relevant to weather derivatives.

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