Stationary distribution for the Jacobi equation with a large random curvature parameter

Abstract

A generalization of the results obtained previously for the case when the curvature parameter of the Jacobi equation is a random quantity distributed on a large or infinite interval is proposed. In this case the realization of the numerical algorithm for finding the stationary measure has some features compared to the previously introduced method. These features are mainly due to the finite numerical accuracy and are discussed in this paper together with the corresponding distributions. These distributions are used to calculate the Lyapunov exponent and the growth rate of statistical moments of the Jacobi field.