Stochastic Theories and Deterministic Differential Equations
Journal article, Peer reviewed
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OriginalversjonMoxnes, J.F., Hausken, K. (2010) Stochastic Theories and Deterministic Differential Equations, Advances in Mathematical Physics. Article ID 749306. 10.1155/2010/749306
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.