Parametric subordination in fractional diffusion processes
Parametric subordination in fractional diffusion processes
复制标题
分数扩散过程中的参数从属关系
DOI：
--
复制
发表时间：
2012
期刊：
影响因子：
--
通讯作者：
F. Mainardi
中科院分区：
文献类型：
--
作者：
R. Gorenflo;F. Mainardi
我们考虑空间一维时空分数扩散的模拟。而在我们之前的一篇论文中(Eur。理论物理。J.专题，第193卷，119-132 (2011)；E-print: http://arxiv.org/abs/1104.4041)，我们已经发展了我们称之为参数从属的基本理论，通过三倍分裂应用于连续时间随机行走，随后通过扩散极限，在这里我们走相反的路。通过傅里叶-拉普拉斯对相关分数阶偏微分演化方程的操作，我们得到了从属积分公式，它告诉我们如何通过首先从物理时间生成操作时间，然后在操作时间中生成空间路径来构建粒子路径。通过将操作时间由物理时间生成反推，得到了参数从属的方法。由于稳定次级的无限可分性，我们可以通过离散化来模拟粒子路径，其中路径的生成点是真实路径的精确快照。通过细化离散化，可以看到越来越多的路径细节。电子印刷基于S.C. Lim， J. Klafter和R. Metzler（编辑）的第10章更新版本，第227-261页：分数动力学，最新进展，世界科学，新加坡2012 （ISBN 9814340588, 9789814340588）。
We consider simulation of spatially one-dimensional space-time fractional diffusion. Whereas in an earlier paper of ours (Eur. Phys. J. Special Topics, Vol. 193, 119–132 (2011); E-print: http://arxiv.org/abs/1104.4041), we have developed the basic theory of what we call parametric subordination via three-fold splitting applied to continuous time random walk with subsequent passage to the diffusion limit, here we go the opposite way. Via Fourier-Laplace manipulations of the relevant fractional partial differential equation of evolution we obtain the subordination integral formula that teaches us how a particle path can be constructed by first generating the operational time from the physical time and then generating in operational time the spatial path. By inverting the generation of operational time from physical time we arrive at the method of parametric subordination. Due to the infinite divisibility of the stable subordinator we can simulate particle paths by discretization where the generated points of a path are precise snapshots of a true path. By refining the discretization more and more fine details of a path become visible. E-print based on an updated version of Chapter 10, pp 227-261 in S.C. Lim, J. Klafter and R. Metzler (Editors): Fractional Dynamics, Recent Advances, World Scientific, Singapore 2012 (ISBN 9814340588, 9789814340588),