Evolution Times of Probability Distributions and Averages—Exact Solutions of the Kramers' Problem

The aim of this chapter is to describe approaches of obtaining exact time characteristics of diffusion stochastic processes (Markov processes) that are in fact a generalization of first passage time (FPT) approach and are based on the definition of characteristic timescale of evolution of an observable as integral relaxation time. These approaches allow us to express the required timescales and to obtain almost exactly the evolution of probability and averages of stochastic processes in really wide range of parameters.