Advances in Mathematical Physics
Volume 2010 (2010), Article ID 749306, 29 pages
doi:10.1155/2010/749306
Research Article

Stochastic Theories and Deterministic Differential Equations

John F. Moxnes1 and Kjell Hausken2

1Department for Protection, Norwegian Defence Research Establishment, P.O. Box 25, 2007 Kjeller, Norway
2Faculty of Social Sciences, University of Stavanger, 4036 Stavanger, Norway

Received 3 January 2010; Accepted 6 May 2010

Academic Editor: Nakao Hayashi

Copyright © 2010 John F. Moxnes and Kjell Hausken. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We discuss the concept of “hydrodynamic” stochastic theory, which is not based on the traditional Markovian concept. A Wigner function developed for friction is used for the study of operators in quantum physics, and for the construction of a quantum equation with friction. We compare this theory with the quantum theory, the Liouville process, and the Ornstein-Uhlenbeck process. Analytical and numerical examples are presented and compared.