Itô versus Stratonovich
Itô versus Stratonovich
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DOI：
10.1007/bf01007642
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发表时间：
1981
影响因子：
1.6
通讯作者：
N. G. Kampen
中科院分区：
文献类型：
--
作者：
N. G. Kampen
本文综述了非线性朗之万或伊藤方程的有关事实和幻想。实际上，它只是一个预方程，当加入解释规则时，它就变成了一个方程。伊藤和斯特拉托诺维奇的规则不同，但两者在数学上是一致的，因此同样可以接受。它们似乎导致物理差异的原因是，用于得出方程的朗之万方法涉及一个默认的假设。对于具有外部噪声的系统，这一假设是合理的，并且很明显Stratonovich规则适用。然而，具有内部噪声的系统只能用主方程来恰当地描述，伊藤-斯特拉托诺维奇的争论永远不会出现。之后，人们可以自由地用伊藤或斯特拉托诺维奇方案来模拟由此产生的波动，但这并不会导致任何新的信息。
A survey is given of the facts and fancies concerning the nonlinear Langevin or Itô equation. Actually, it is merely a pre-equation, which becomes an equation when an interpretation rule is added. The rules of Itô and Stratonovich differ, but both are mathematically consistent and therefore equally admissible conventions. The reason why they seem to lead to physical differences is that the Langevin approach used to arrive at the equation involves a tacit assumption. For systems with external noise this assumption can be justified, and it is then clear that the Stratonovich rule applies. Systems with internal noise, however, can only be properly described by a master equation and the Itô-Stratonovich controversy never enters. Afterward one is free to model the resulting fluctuations either with an Itô or a Stratonovich scheme, but that does not lead to any new information.