论文标题
分数主方程，集合自我强化和强烈记忆效应的种群异质性
Population heterogeneity in the fractional master equation, ensemble self-reinforcement and strong memory effects
论文作者
论文摘要
我们在连续的时间内制定了分数主方程，并在随机步行者的种群中随机过渡概率，以便有效的基础随机步行表现出合奏的自我强化。人口异质性产生了随机步行，其条件过渡概率随着以前采取的步骤数量而增加（自我强化）。通过此，我们建立了与异质集合的随机步行之间的联系，而在过渡概率取决于步骤的整个历史的情况下，它们具有强烈的内存。我们发现，通过从属方程式的分数泊机方程的平均解决方案，涉及分数泊松过程，计算给定时间时的步骤数，以及具有自我强化的基本离散随机步行。我们还找到了方差的精确解决方案，即使分数指数趋向于1。
We formulate a fractional master equation in continuous time with random transition probabilities across the population of random walkers such that the effective underlying random walk exhibits ensemble self-reinforcement. The population heterogeneity generates a random walk with conditional transition probabilities that increase with the number of steps taken previously (self-reinforcement). Through this, we establish the connection between random walks with a heterogeneous ensemble and those with strong memory where the transition probability depends on the entire history of steps. We find the ensemble averaged solution of the fractional master equation through subordination involving the fractional Poisson process counting the number of steps at a given time and the underlying discrete random walk with self-reinforcement. We also find the exact solution for the variance which exhibits superdiffusion even as the fractional exponent tends to 1.
