论文标题
连续时间的大偏差随机步行
Large Deviation in Continuous Time Random Walks
论文作者
论文摘要
我们讨论连续时间随机步行（CTRW）的较大偏差特性，并就CTRW中较大偏差率的一般表达方式，就步骤长度和等待时间的分布的相应速率而言。在高斯分布的情况下，一般表达式将一般表达式降低到应用于等待时间的累积生成函数的两个legendre变换的序列。讨论了几个例子（Bernoulli和Gaussian随机步行，具有指数分布的等待时间，具有单面Lévy和Pareto-Distribed等待时间的高斯随机步行）揭示了如此巨大的偏差的有趣一般特性。
We discuss large deviation properties of continuous-time random walks (CTRW) and present a general expression for the large deviation rate in CTRW in terms of the corresponding rates for the distributions of steps' lengths and waiting times. In the case of Gaussian distribution of steps' lengths the general expression reduces to a sequence of two Legendre transformations applied to the cumulant generating function of waiting times. The discussion of several examples (Bernoulli and Gaussian random walks with exponentially distributed waiting times, Gaussian random walks with one-sided Lévy and Pareto-distributed waiting times) reveals interesting general properties of such large deviations.
