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

Silvia Vitali, Iva Budimir, Claudio Runfola and Gastone Castellani
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Silvia Vitali: Department of Physics and Astronomy; University of Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy
Iva Budimir: Department of Physics and Astronomy; University of Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy
Claudio Runfola: Department of Physics and Astronomy; University of Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy
Gastone Castellani: Department of Physics and Astronomy; University of Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy

Mathematics, 2019, vol. 7, issue 12, 1-9

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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