Deceased.
Evolution Times of Probability Distributions and Averages—Exact Solutions of the Kramers' Problem
- I. Prigogine3,4,
- Stuart A. Rice5
Published Online: 28 APR 2002
DOI: 10.1002/0471264318.ch6
Copyright © 2002 John Wiley & Sons, Inc.
Book Title
Advances in Chemical Physics, Volume 121
Additional Information
How to Cite
Malakhov, A. N. and Pankratov, A. L. (2002) Evolution Times of Probability Distributions and Averages—Exact Solutions of the Kramers' Problem, in Advances in Chemical Physics, Volume 121 (eds I. Prigogine and S. A. Rice), John Wiley & Sons, Inc., New York, USA. doi: 10.1002/0471264318.ch6
Editor Information
- 3
Center for Studies in Statistical Mechanics and Complex Systems, The University of Texas, Austin, Texas, USA
- 4
International Solvay Institutes, Université Libre de Bruxelles, Brussels, Belgium
- 5
Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois, USA
Publication History
- Published Online: 28 APR 2002
- Published Print: 4 JAN 2002
Book Series:
Book Series Editors:
- I. Prigogine3,4,
- Stuart A. Rice5
Series Editor Information
- 3
Center for Studies in Statistical Mechanics and Complex Systems, The University of Texas, Austin, Texas, USA
- 4
International Solvay Institutes, Université Libre de Bruxelles, Brussels, Belgium
- 5
Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois, USA
ISBN Information
Print ISBN: 9780471205043
Online ISBN: 9780471264316
- Summary
- Chapter
Keywords:
- probability distributions;
- probability averages;
- evolution times;
- Kramers' problem;
- random processes;
- escape time calculation;
- first passage time (FPT) approach
Summary
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.