Large-deviation functions for nonlinear functionals of a Gaussian stationary Markov process

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(o)(T)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) similar toexp[-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.