标题： 布朗子ordinator和分数阶柯西问题 显示英文标题

标题： Brownian subordinators and fractional Cauchy problems

摘要： 布朗时间过程是一种马尔可夫过程，它由一个独立的一维布朗运动的绝对值来支配。 它的转移密度函数解决了涉及原始马尔可夫过程生成元平方的一个初值问题。 看似无关的一类过程，作为连续时间随机游走的尺度极限出现，涉及到经典的稳定子ordinator的逆时过程或击中时过程的次序。 由此产生的密度函数解出了分数阶柯西问题，这是一种扩展，涉及时间上的分数阶导数。 在本文中，我们将展示这两类过程之间紧密而意想不到的联系，从而得出这两组偏微分方程之间的等价性。 显示英文摘要

摘要： A Brownian time process is a Markov process subordinated to the absolute value of an independent one-dimensional Brownian motion. Its transition densities solve an initial value problem involving the square of the generator of the original Markov process. An apparently unrelated class of processes, emerging as the scaling limits of continuous time random walks, involve subordination to the inverse or hitting time process of a classical stable subordinator. The resulting densities solve fractional Cauchy problems, an extension that involves fractional derivatives in time. In this paper, we will show a close and unexpected connection between these two classes of processes, and consequently, an equivalence between these two families of partial differential equations.