Lagging/Leading Coupled Continuous Time Random Walks, Renewal Times and their Joint Limits
Lagging/Leading Coupled Continuous Time Random Walks, Renewal Times and their Joint Limits
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滞后/超前耦合连续时间随机游走、更新时间及其联合极限
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
B. Henry
中科院分区：
文献类型：
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作者：
P. Straka;B. Henry
服从一个随机游走更新过程产生一个连续时间随机游走（CTRW）模型的扩散，包括异常扩散的可能性。幂律CTRW标度极限的跃迁密度已被证明可以求解分数阶Fokker-Planck方程。我们考虑的限制时出现的等待时间和跳跃从一个无穷小的三角形阵列的CTRW序列。当等待时间在跳跃之前或之后时，我们分别识别出两个不同的极限过程$X_t$和$Y_t$。在极限过程中，我们跟踪的CTRW的更新时间，从而找到两个极限过程。最后，我们计算了所有四个极限过程在一个固定的时间$t$评估的联合法律。
Subordinating a random walk to a renewal process yields a continuous time random walk (CTRW) model for diffusion, including the possibility of anomalous diffusion. Transition densities of scaling limits of power law CTRWs have been shown to solve fractional Fokker-Planck equations. We consider limits of sequences of CTRWs which arise when both waiting times and jumps are taken from an infinitesimal triangular array. We identify two different limit processes $X_t$ and $Y_t$ when waiting times precede or follow jumps, respectively. In the limiting procedure, we keep track of the renewal times of the CTRWs and hence find two more limit processes. Finally, we calculate the joint law of all four limit processes evaluated at a fixed time $t$.