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首页> 外文期刊>Physica Scripta: An International Journal for Experimental and Theoretical Physics >Extensions of the Novikov-Furutsu theorem, obtained by using Volterra functional calculus
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Extensions of the Novikov-Furutsu theorem, obtained by using Volterra functional calculus

机译：通过使用Volterra功能微积分获得的NoviCov-Furutsu定理的扩展

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摘要

The Novikov-Furutsu (NF) theorem is a well-known mathematical tool, used in stochastic dynamics for correlation splitting, that is, for evaluating the mean value of the product of a random functional with a Gaussian argument multiplied by the argument itself. In this work, the NF theorem is extended for mappings (function-functionals) of two arguments, one being a random variable and the other a random function, both of which are Gaussian, may have non-zero mean values, and may be correlated with each other. This extension allows for the study of random differential equations under coloured noise excitation, which may be correlated with the random initial value. Applications in this direction are briefly discussed. The proof of the extended NF theorem is based on a more general result, also proven herein by using Volterra functional calculus, stating that: the mean value of a general, nonlinear function-functional having random arguments, possibly non-Gaussian, can be expressed in terms of the characteristic functional of its arguments. Generalizations to the multidimensional case (multivariate random arguments) are also presented.
机译：NoviTov-Furutsu（NF）定理是一种众所周知的数学工具，用于随机动力学用于相关性分裂，即，用于评估随机函数的乘积的乘积的平均值，与高斯参数乘以参数本身。在这项工作中，对于两个参数的映射（函数函数）扩展了NF定理，一个是随机变量，另一个是高斯的随机函数，可以具有非零平均值，并且可能是相关的彼此。该扩展允许在有色噪声激励下研究随机微分方程，其可以与随机初始值相关。简要讨论了此方向的应用。扩展NF定理的证据基于更一般的结果，通过使用Volterra功能微积分，陈述：可以表达：可以表达具有随机参数的一般的平均值，可能是非高斯的一般的平均值，可能是非高斯的。就其论点的特征功能而言。还提出了对多维案例（多变量随机参数）的概括。

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