Non-equilibrium solutions of an infinite system of stochastic differential equations

2005 ◽  
pp. 297-303 ◽  
Author(s):  
Hermann Rost
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Infinite System ◽  
Equilibrium Solutions ◽  
Non Equilibrium

Approximation theorem for stochastic differential equations with interaction

2003 ◽  
Vol 11 (3) ◽  
Author(s):  
A. Yu. Pilipenko
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Infinite System ◽  
Approximation Theorem

The approximation theorem for an infinite system of interacting stochastic differential equations is proved. This result is applied then for describing the support of the distribution of the solution of this system.

A MICROSCOPIC DERIVATION OF STOCHASTIC DIFFERENTIAL EQUATIONS

1996 ◽  
Vol 10 (13n14) ◽  
pp. 1585-1597
Author(s):  
TOSHIHICO ARIMITSU
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Quantum Systems ◽  
The Other ◽  
Operator Formalism ◽  
Canonical Operator ◽  
Thermo Field Dynamics ◽  
Microscopic Derivation ◽  
Non Equilibrium

With the help of the formulation of Non-Equilibrium Thermo Field Dynamics, constructed is a unified canonical operator formalism for the quantum stochastic differential equations. In the course of its construction, it is found that there are at least two formulations, i.e. one is non-hermitian and the other is hermitian. Having been settled the framework which should be satisfied by the quantum stochastic differential equations, performed is a microscopic derivation of these stochastic differential equations by extending the projector methods. This investigation may open a new field for quantum systems in order to understand the deeper meaning of dissipation.

Stochastic Differential Equations for Power Law Behaviors

2012 ◽  
Author(s):  
Bo Jiang ◽  
Roger Brockett ◽  
Weibo Gong ◽  
Don Towsley
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Power Law
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