Estimates of probabilities of large deviations in problems of estimation of calculated actions. I

Abstract

Let there be given a velocity field described by some function that depends both on time and a point of a phase space. It is assumed that the velocity field is subject to small random perturbations that are, in the general case, generalized derivatives of a pre-Gaussian process.

On the basis of observations of trajetories of the motion of the system in such a random environment, we would like to recover the given velocity field. We obtain a nuclear estimate of the velocity vector. Deviations of the estimate from the estimated quantity are controlled by means of exponential S. N. Berstein inequalities.