A New Expansion of Dynamical Correlations in Stochastic Processes and Chaotic Dynamics

Abstract

A new expansion method to obtain time correlation functions and large deviation statistical characteristic functions in Markovian stochastic processes and chaotic dynamics is proposed. Because for chaotic dynamics no smooth, steady-state probability density exists, it is not convenient for formulating the problem of solving the eigenvalue problem to the time evolution operator. Instead, we use the Mori projection operator method with an operator projected on a state space larger than that spanned by the dynamical variable under consideration. Choosing the number of additional dynamical variables, we can systematically control the degree of approximations.