双重随机连续时间随机游走
Doubly stochastic continuous time random walk
AI总结：
针对 Montroll-Weiss 连续时间随机游走无法解释随机扩散性波动的问题，本文提出双重随机版本，用波动的跳跃率替代等待时间，在保持可处理性的同时揭示了丰富现象，为布朗但非高斯扩散提供了替代路径。
摘要：
自大约六十年前提出以来，Montroll-Weiss 连续时间随机游走因其易用性及描述常规扩散和反常扩散的能力而获得了广泛应用。然而，尽管具有广泛的适用性和通用性，该模型无法解释源自随机扩散性波动的效应，而这些波动已在资产价格和分子的运动中被观察到。为了弥补这一空白，我们引入了该模型的双重随机版本，其中跳跃之间的等待时间被波动的跳跃率所取代。我们证明，这层新加入的随机性产生了丰富的现象学特征，同时保持了模型的完全可处理性——这使我们能够探索其一般性质并通过实例加以说明。特别地，我们表明本文提出的模型为布朗但非高斯扩散提供了一条替代路径，而这种现象此前已通过扩散性扩散方法被观察和解释。
英文摘要：
Since its introduction, some sixty years ago, the Montroll-Weiss continuous time random walk has found numerous applications due its ease of use and ability to describe both regular and anomalous diffusion. Yet, despite its broad applicability and generality, the model cannot account for effects coming from random diffusivity fluctuations which have been observed in the motion of asset prices and molecules. To bridge this gap, we introduce a doubly stochastic version of the model in which waiting times between jumps are replaced with a fluctuating jump rate. We show that this newly added layer of randomness gives rise to a rich phenomenology while keeping the model fully tractable -- allowing us to explore general properties and illustrate them with examples. In particular, we show that the model presented herein provides an alternative pathway to Brownian yet non-Gaussian diffusion which has been observed and explained via diffusing diffusivity approaches.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
