Linear combinations of i.i.d. strictly stable variables with random coefficients and their application to anomalous diffusion processes

Scott Hottovy and Gianni Pagnini

Physica A: Statistical Mechanics and its Applications, 2024, vol. 647, issue C

Abstract: We show that linear combinations of independent and identically distributed strictly stable variables with positive random coefficients is equal in distribution to a function of these random coefficients times a random variable from the same stable distribution. Furthermore, this result is used to show that a random linear combination of independent standard Wiener processes has the distribution of a function of these random coefficients times one standard Wiener process. In opposition to the central limit theorem, this result does not require a large number of terms but it holds with two or more terms. This has implications to simplify stochastic differential equations with a finite number of noises with random coefficients that can be used in modeling anomalous diffusion.

Keywords: Linear combinations; Random coefficients; Strictly stable variables; Wiener process (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:647:y:2024:i:c:s0378437124004217

DOI: 10.1016/j.physa.2024.129912

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