重温Lévy walk：Hermite多项式展开方法
Lévy walk revisited: Hermite polynomial expansion approach
摘要：
积分变换法（傅立叶变换或拉普拉斯变换等）是对随机过程进行理论分析的有效方法。然而，对于时空耦合的情况，例如，在Lévy walk或非线性情况下，积分变换法可能会失效，甚至不再起作用。这里我们提供了Hermite多项式展开法，作为积分变换法的补充。用Hermite多项式展开法计算了一般Lévy游动的一些统计观测量，并在积分变换法和新引入的方法都适用的情况下进行了比较.
英文摘要：
Integral transform method (Fourier or Laplace transform, etc) is more often effective to do the theoretical analysis for the stochastic processes. However, for the time-space coupled cases, e.g., Lévy walk or nonlinear cases, integral transform method may fail to be so strong or even do not work again. Here we provide Hermite polynomial expansion approach, being complementary to integral transform method. Some statistical observables of general Lévy walks are calculated by the Hermite polynomial expansion approach, and the comparisons are made when both the integral transform method and the newly introduced approach work well.
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