非独立连续时间随机游动
Non-independent continuous time random walks
摘要：
连续时间随机游走（CTRW）的一般发展假设跳跃和时间间隔是一组独立同分布的二维随机变量。在本文中，我们解决了非独立的CTRW的连续跳跃和/或时间间隔相关的理论设置。一个精确的解决方案的问题，获得了特殊的，但相关的情况下，其中的相关性只取决于连续跳跃的迹象。即使在这种简单的情况下，一些有趣的功能出现，如从单峰到双峰分布的过渡，由于相关性。我们还开发了必要的分析技术和近似值，以处理实践中可能出现的更一般的情况。
英文摘要：
The usual development of the continuous time random walk (CTRW) assumes that jumps and time intervals are a two-dimensional set of independent and identically distributed random variables. In this paper we address the theoretical setting of non-independent CTRW's where consecutive jumps and/or time intervals are correlated. An exact solution to the problem is obtained for the special but relevant case in which the correlation solely depends on the signs of consecutive jumps. Even in this simple case some interesting features arise such as transitions from unimodal to bimodal distributions due to correlation. We also develop the necessary analytical techniques and approximations to handle more general situations that can appear in practice.
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