Stochastic Theories and Deterministic Differential Equations
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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.
Moxnes, John Fredrik; Hausken, Kjell. Stochastic Theories and Deterministic Differential Equations. Advances in Mathematical Physics 2010 s. -