Delay Fokker-Planck equations, Novikov's theorem, and Boltzmann distributions as small delay approximations
Delay Fokker-Planck equations, Novikov's theorem, and Boltzmann distributions as small delay approximations
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DOI：
10.1103/physreve.72.011112
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发表时间：
2005-07-01
影响因子：
2.4
通讯作者：
Frank, TD
中科院分区：
文献类型：
--
作者：
Frank, TD
我们研究的时滞随机系统，可以通过所谓的延迟福克-普朗克方程。利用Novikov定理，我们首先证明了延迟Fokker-Planck方程理论与普通Fokker-Planck方程理论是平等的。随后，我们得到平稳分布的情况下，小的时间延迟。在加性噪声系统的情况下，这些分布可以被转换成包含有效势函数的玻尔兹曼分布的形式。
We study time-delayed stochastic systems that can be described by means of so-called delay Fokker-Planck equations. Using Novikov's theorem, we first show that the theory of delay Fokker-Planck equations is on an equal footing with the theory of ordinary Fokker-Planck equations. Subsequently, we derive stationary distributions in the case of small time delays. In the case of additive noise systems, these distributions can be cast into the form of Boltzmann distributions involving effective potential functions.