与分布阶微积分、从属算子和慢扩散有关的Lévy混合
Lévy mixing related to distributed order calculus, subordinators and slow diffusions
摘要：
分布阶微积分的研究通常涉及到$\int_0^1 \partial^αu \, m(dα)$形式的分数阶导数，对于某种测度$m$，最终是一种概率测度。本文提出了一种基于Lévy混合的方法。考虑了与$ła(y), b(y), ν(ds, y) \r$形式的Lévy三元组相关的非减Lévy过程，并利用概率测度将参数$y$随机化.从不同的角度研究了相关的从属关系。得到了一些分布性质，并探讨了马尔可夫过程与逆局部时的相互作用。分布顺序积分-微分算子的引入和采用，以明确地写这样的过程的控制方程。慢扩散的应用进行了讨论。
英文摘要：
The study of distributed order calculus usually concerns about fractional derivatives of the form $\int_0^1 \partial^αu \, m(dα)$ for some measure $m$, eventually a probability measure. In this paper an approach based on Lévy mixing is proposed. Non-decreasing Lévy processes associated to Lévy triplets of the form $ła(y), b(y), ν(ds, y) \r$ are considered and the parameter $y$ is randomized by means of a probability measure. The related subordinators are studied from different point of views. Some distributional properties are obtained and the interplay with inverse local times of Markov processes is explored. Distributed order integro-differential operators are introduced and adopted in order to write explicitly the governing equations of such processes. An application to slow diffusions is discussed.
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