非均匀介质中截断Lévy飞行扩散的拉伸高斯渐近性
Stretched-Gaussian asymptotics of the truncated Lévy flights for the diffusion in nonhomogeneous media
摘要：
考虑了由跳跃规模分布和等待时间分布定义的Lévy跳跃过程。跳跃率取决于过程值。在扩散极限下求解了含有可变扩散系数的分数阶扩散方程。当序参量$μ\to2$。引入了截断指数和幂律形式的Lévy飞行，并利用Monte Carlo方法模拟了相应的随机游走过程。在这两种情况下，拉伸高斯尾巴。到达极限分布所需的时间强烈地依赖于跳跃率参数。当截止函数缓慢下降时，分布的尾部似乎是代数的。
英文摘要：
The Lévy, jumping process, defined in terms of the jumping size distribution and the waiting time distribution, is considered. The jumping rate depends on the process value. The fractional diffusion equation, which contains the variable diffusion coefficient, is solved in the diffusion limit. That solution resolves itself to the stretched Gaussian when the order parameter $μ\to2$. The truncation of the Lévy flights, in the exponential and power-law form, is introduced and the corresponding random walk process is simulated by the Monte Carlo method. The stretched Gaussian tails are found in both cases. The time which is needed to reach the limiting distribution strongly depends on the jumping rate parameter. When the cutoff function falls slowly, the tail of the distribution appears to be algebraic.
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