Vitali, S.; Budimir, I.; Runfola, C.; Castellani, G. The Role of the Central Limit Theorem in the Heterogeneous Ensemble of Brownian Particles Approach. Mathematics2019, 7, 1145.
Vitali, S.; Budimir, I.; Runfola, C.; Castellani, G. The Role of the Central Limit Theorem in the Heterogeneous Ensemble of Brownian Particles Approach. Mathematics 2019, 7, 1145.
Vitali, S.; Budimir, I.; Runfola, C.; Castellani, G. The Role of the Central Limit Theorem in the Heterogeneous Ensemble of Brownian Particles Approach. Mathematics2019, 7, 1145.
Vitali, S.; Budimir, I.; Runfola, C.; Castellani, G. The Role of the Central Limit Theorem in the Heterogeneous Ensemble of Brownian Particles Approach. Mathematics 2019, 7, 1145.
Abstract
The central limit theorem (CLT) and its generalization to stable distributions have been widely described in literature. However, many variations of the theorem have been defined and often their applicability in practical situations is not straightforward. In particular, the applicability of the CLT is essential for a derivation of heterogeneous ensemble of Brownian particles (HEBP). Here, we analyze the role of the CLT within the HEBP approach in more detail and derive the conditions under which the existing theorems are valid.
Keywords
central limit theorem; anomalous diffusion; stable distribution; fractional calculus; power law
Subject
Computer Science and Mathematics, Probability and Statistics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
