Limit theorem for continuous-time random walks with two time scales
Limit theorem for continuous-time random walks with two time scales
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DOI：
10.1239/jap/1082999078
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发表时间：
2004-06-01
影响因子：
1
通讯作者：
Scheffler, HP
中科院分区：
文献类型：
--
作者：
Becker-Kern, P;Meerschaert, MM;Scheffler, HP
连续时间随机行走包含了随机跳跃之间的随机等待时间。它们在物理学中被用来为粒子运动建模。实际重封使用两种不同的时标来表示平均等待时间和与平均值的偏差。本文推导出了这类过程的尺度极限。这些极限过程由可能在物理学中有用的分数偏微分方程所支配。还得到了随机过程有限维分布弱收敛的一个转移定理。
Continuous-time random walks incorporate a random waiting time between random jumps. They are used in physics to model particle motion. A physically realistic resealing uses two different time scales for the mean waiting time and the deviation from the mean. This paper derives the scaling limits for such processes. These limit processes are governed by fractional partial differential equations that may be useful in physics. A transfer theorem for weak convergence of finite-dimensional distributions of stochastic processes is also obtained.