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The Role of the Central Limit Theorem in the Heterogeneous Ensemble of Brownian Particles Approach

Department of Physics and Astronomy; University of Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy
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These authors contributed equally to this work.
Mathematics 2019, 7(12), 1145; https://doi.org/10.3390/math7121145
Received: 12 October 2019 / Revised: 15 November 2019 / Accepted: 21 November 2019 / Published: 23 November 2019
(This article belongs to the Special Issue Advanced Mathematical Methods: Theory and Applications)
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. View Full-Text
Keywords: central limit theorem; anomalous diffusion; stable distribution; fractional calculus; power law central limit theorem; anomalous diffusion; stable distribution; fractional calculus; power law
MDPI and ACS Style

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.

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