几何光学中湍流折射的分数布朗运动性质
The fractional Brownian motion property of the turbulent refractive within Geometric Optics
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。这些过程允许重建大部分折射率特性，但它们是不可微的。我们克服了明显的不可能性，它们的使用在射线光学近似引入随机微积分。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，它的影响在实验数据的统计分析进行了讨论。特别是，我们分析了一个简单的传播问题的特征变量的平均解的依赖性。
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 refractive index properties, but they are not differentiable. We overcome the apparent impossibility of their use within the Ray Optics approximation introducing 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. In particular, we analyze the dependence of the averaged solution against the characteristic variables of a simple propagation problem.
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