On the principle of minimum growth rate in multiplicatively interacting stochastic processes

2006/08/08 by Akihiro Fujihara, Fujihara, Akihiro, Toshiya Ohtsuki +3
Economics, Econometrics and Finance · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Complex Network Analysis Techniques #Complex Systems and Time Series Analysis #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech

paper · pdf · doi:10.48550/arxiv.cond-mat/0608205

5 pages, 2 figures

arxiv created 2006/08/08 · openalex publication_date 2006/08/08 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

A method of moment inequalities is used to derive the principle of minimum growth rate in multiplicatively interacting stochastic processes(MISPs). When a value of a power-law exponent at the tail of probability distribution function exists in a range 0 < s ≤ 1, a first-order moment diverges and an equality for a growth rate of systems breaks down. From the estimate of inequalities, we newly find a conditional inequality which determines the growth rate, and then the exponent in 0 < s ≤ 1.

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