多尺度Lévy过程的显式表示和多重分形守恒律的渐近性
Explicit representations for multiscale Lévy processes, and asymptotics of multifractal conservation laws
摘要：
由Lévy过程驱动的非线性守恒律的解，在超临界非线性的情况下，具有由线性化方程的解决定的渐进行为。因此，后者的显式表示在非线性理论中是有意义的。在本文中，我们集中在的情况下，驱动Lévy过程是一个多尺度稳定（反常）扩散，这对应的情况下考虑的多重分形守恒律在[1-4]。显式表示，建立在以前的工作单尺度问题（见，例如，[5])的特殊函数（如MeijerG函数）的发展，并服从于直接数值计算的相关概率。
英文摘要：
Nonlinear conservation laws driven by Lévy processes have solutions which, in the case of supercritical nonlinearities, have an asymptotic behavior dictated by the solutions of the linearized equations. Thus the explicit representation of the latter is of interest in the nonlinear theory. In this paper we concentrate on the case where the driving Lévy process is a multiscale stable (anomalous) diffusion, which corresponds to the case of multifractal conservation laws considered in [1-4]. The explicit representations, building on the previous work on single-scale problems (see, e.g.,[5]), are developed in terms of the special functions (such as Meijer G functions), and are amenable to direct numerical evaluations of relevant probabilities.
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