标度指数的合成：分数阶Levy模型
Synthesis of scaling exponents: a fractional Levy model
摘要：
曼德尔布罗特引入了分形的概念来描述自然世界许多方面的非欧几里得形状。在时间序列方面，他提出使用分数布朗运动（fBM）来模拟不可忽略的时间持续性，即“约瑟夫效应”;并提出使用利维飞行来量化大的不连续性，即“诺亚效应”。在空间物理学中，这两种效应都表现在地磁指数及其太阳风驱动因素的不稳定性和长程相关性上，而这两个特征目前已得到公认。为了在一个紧凑的模型中捕获和量化Noah和Joseph效应，我们提出了“桥接”分数Levy运动（fLm）在空间物理学中的应用。我们在这个范例中执行一些以前的缩放结果的初步评估，并显示如何fLm可以模拟以前观察到的指数。我们为未来提出了一些新的方向。
英文摘要：
Mandelbrot introduced the concept of fractals to describe the non-Euclidean shape of many aspects of the natural world. In the time series context he proposed the use of fractional Brownian motion (fBm) to model non-negligible temporal persistence, the "Joseph Effect"; and Levy flights to quantify large discontinuities, the "Noah Effect". In space physics, both effects are manifested in the intermittency and long-range correlation which are by now well-established features of geomagnetic indices and their solar wind drivers. In order to capture and quantify the Noah and Joseph effects in one compact model we propose the application of the "bridging" fractional Levy motion (fLm) to space physics. We perform an initial evaluation of some previous scaling results in this paradigm, and show how fLm can model the previously observed exponents. We suggest some new directions for the future.
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