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非独立连续时间随机游走。

Nonindependent continuous-time random walks.

作者信息

Montero Miquel, Masoliver Jaume

机构信息

Departament de Física Fonamental, Universitat de Barcelona, Diagonal 647, Barcelona, Spain.

出版信息

Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Dec;76(6 Pt 1):061115. doi: 10.1103/PhysRevE.76.061115. Epub 2007 Dec 13.

Abstract

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 nonindependent CTRWs 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.

摘要

连续时间随机游走(CTRW)的通常发展假设跳跃和时间间隔是一组二维独立同分布随机变量。在本文中,我们探讨非独立CTRW的理论设置,其中连续跳跃和/或时间间隔是相关的。对于相关性仅取决于连续跳跃符号的特殊但相关的情况,我们得到了该问题的精确解。即使在这种简单情况下,也会出现一些有趣的特征,例如由于相关性导致的从单峰分布到双峰分布的转变。我们还开发了必要的分析技术和近似方法,以处理实际中可能出现的更一般情况。

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