Stochastic Theories and Deterministic Differential Equations | Zendy

John F. Moxnes | Zendy; Kjell Hausken | Zendy

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Stochastic Theories and Deterministic Differential Equations

Author(s) -

John F. Moxnes,

Kjell Hausken

Publication year - 2010

Publication title -

advances in mathematical physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.283

H-Index - 23

eISSN - 1687-9139

pISSN - 1687-9120

DOI - 10.1155/2010/749306

Subject(s) - stochastic differential equation , quantum , statistical physics , mathematics , markov process , quantum stochastic calculus , stochastic process , ornstein–uhlenbeck process , function (biology) , quantum probability , master equation , differential equation , quantum process , physics , mathematical analysis , quantum mechanics , quantum dynamics , statistics , evolutionary biology , biology

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

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