湍流refractive index的分数布朗运动性质与Fermat极值原理
The fractional Brownian motion property of the turbulent refractive index and the Fermat's Extremal Principle
摘要：
我们引入分数布朗运动过程（fBM）作为湍流折射率的替代模型。这些过程允许重构大多数索引属性，但它们是不可微的。我们克服了明显的不可能性，他们使用的变分方程来自费马原理的引入随机微积分。之后，我们成功地提供了一个解决方案的随机射线方程，此外，它的含义在实验数据的统计分析进行了讨论。
英文摘要：
We introduce fractional Brownian motion processes (fBm) as an alternative model for the turbulent index of refraction. These processes allow to reconstruct most of the index properties, but they are not differentiable. We overcome the apparent impossibility of their use in the variational equation coming from the Fermat's Principle with the introduction of a Stochastic Calculus. Afterwards, we successfully provide a solution for the stochastic ray equation; moreover, its implications in the statistical analysis of experimental data is discussed.
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