用一种分数阶算法研究非马尔可夫过程中阻尼与涨落的竞争机制

基于分数阶朗之万方程和随机行走理论, 建立了一种用于研究非马尔可夫系统中随机变量随时间演化的数值模拟算法, 称之为分数阶随机行走模拟法. 进一步运用此算法分别数值研究了无阻尼有涨落、 有阻尼无涨落和阻尼与涨落兼备三种情况下, 受欠扩散分数阶朗之万方程约束的随机变量随时间的演化行为. 结果显示阻尼和涨落存在竞争关系: 高斯型涨落的影响会随着时间的增长被"抹平", 从而凸显阻尼使系统趋于平衡的作用; 而长尾型涨落则由于包含"小概率大贡献"事件, 使得长时间演化之后系统变量仍以一定概率出现突然变化.关键词：非马尔可夫欠扩散阻尼与涨落分数阶朗之万方程

Application of a fractional algorithm to studying the competition between dissipation and fluctuation in non-Markov process

Based on fractional Langevin equation and random walk theory, a numerical algorithm that can be applied to non-Markov long-memory system is established in this paper. In addition, the evolution behaviour of random variable ruled by fractional sub-diffusion equation is numerically studied in three conditions: no dissipation, no fluctuation and both being present. The results show that competition exists between dissipation and fluctuation. As time goes by, the effect of Guassian fluctuation weakens and damping plays a main role in the evolution of system; however, because of the existance of "rare-though-dominant" events, long-tail fluctuation makes the evolution of system abrupt change at a certain probability.
Keywords：non-Markovsub-diffusiondissipation and fluctuationfractional Langevin equation