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首页> 外文期刊>Physica Scripta: An International Journal for Experimental and Theoretical Physics >A Markov approach to nonlinear multivariate delay systems with noise
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A Markov approach to nonlinear multivariate delay systems with noise

机译：非线性多变量时滞系统的马尔可夫方法

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摘要

It is well known that non-Markov processes can be described by means of Markov processes by increasing the dimension of the non-Markov processes. In line with this approach, we derive a description of multivariate stochastic processes with delay in terms of Markov processes. In particular, a multivariate Langevin equation and the corresponding multivariate Fokker-Planck equation is obtained for multivariate systems with delay. In addition, an evolution equation of the Fokker-Planck type for systems with delay is derived that generalizes the evolution equation proposed by Guillouzic et al. to the multivariate case. Both Ito and Stratonovich calculus are considered. [References: 31]
机译：众所周知，可以通过增加非马尔可夫过程的维数来借助于马尔可夫过程来描述非马尔可夫过程。与这种方法一致，我们根据马尔可夫过程推导了具有延迟的多元随机过程的描述。尤其是，对于具有时滞的多元系统，获得了多元Langevin方程和相应的多元Fokker-Planck方程。此外，推导了具有时滞系统的Fokker-Planck型演化方程，该方程推广了Guillouzic等人提出的演化方程。多元情况。伊托和斯特拉托诺维奇演算都被考虑了。 [参考：31]

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