title: Large-deviation functions for nonlinear functionals of a Gaussian stationary Markov process.
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)integral(T)(0)dT' V[X(T')], where V(X) is an arbitrary function of the stationary Gaussian Markov process X(T). For T-->infinity at fixed r we obtain P(r,T) approximately exp[-theta(r)T], where theta(r) is a large-deviation function. We present explicit results for a number of special cases including V(X)=XH(X) [where H(X) is the Heaviside function], which is related to the cooling and the heating degree days relevant to weather derivatives.
authors.affiliation: Laboratoire de Physique Quantique (UMR C5626 du CNRS), Université Paul Sabatier, 31062 Toulouse Cedex, France.
authors.forename: Satya N
authors.initials: SN
authors.lastname: Majumdar
authors.forename: Alan J
authors.initials: AJ
authors.lastname: Bray