Weron Karina, Stanislavsky Aleksander, Jurlewicz Agnieszka, Meerschaert Mark M, Scheffler Hans-Peter
Institute of Physics, Wrocław University of Technology, Wyb. Wyspiańskiego 27, 50-370 Wrocław, Poland.
Proc Math Phys Eng Sci. 2012 Jun 8;468(2142):1615-1628. doi: 10.1098/rspa.2011.0697. Epub 2012 Feb 1.
We present a class of continuous-time random walks (CTRWs), in which random jumps are separated by random waiting times. The novel feature of these CTRWs is that the jumps are clustered. This introduces a coupled effect, with longer waiting times separating larger jump clusters. We show that the CTRW scaling limits are time-changed processes. Their densities solve two different fractional diffusion equations, depending on whether the waiting time is coupled to the preceding jump, or the following one. These fractional diffusion equations can be used to model all types of experimentally observed two power-law relaxation patterns. The parameters of the scaling limit process determine the power-law exponents and loss peak frequencies.
我们提出了一类连续时间随机游走（CTRW），其中随机跳跃被随机等待时间分隔开。这些CTRW的新颖之处在于跳跃是成簇的。这引入了一种耦合效应，即较长的等待时间分隔较大的跳跃簇。我们表明CTRW标度极限是时间变换过程。它们的密度根据等待时间是与前一个跳跃还是后一个跳跃耦合，求解两个不同的分数阶扩散方程。这些分数阶扩散方程可用于对所有类型的实验观察到的双幂律弛豫模式进行建模。标度极限过程的参数决定了幂律指数和损耗峰值频率。
