Meerschaert Mark M, Straka Peter
Department of Statistics and Probability, Michigan State University, East Lansing, MI 48824,
J Stat Phys. 2012 Nov;149(5):578-886. doi: 10.1007/s10955-012-0638-z.
A continuous time random walk (CTRW) imposes a random waiting time between random particle jumps. CTRW limit densities solve a fractional Fokker-Planck equation, but since the CTRW limit is not Markovian, this is not sufficient to characterize the process. This paper applies continuum renewal theory to restore the Markov property on an expanded state space, and compute the joint CTRW limit density at multiple times.
连续时间随机游走（CTRW）在随机粒子跳跃之间施加了一个随机等待时间。CTRW极限密度可求解一个分数阶福克 - 普朗克方程，但由于CTRW极限不是马尔可夫的，这不足以刻画该过程。本文应用连续更新理论在一个扩展的状态空间上恢复马尔可夫性质，并计算多个时刻的联合CTRW极限密度。
