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

Akihiro Fujihara; Toshiya Ohtsuki; Hiroshi Yamamoto

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

Akihiro Fujihara·Toshiya Ohtsuki·Hiroshi Yamamoto

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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 $0 < s \le 1$, 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 $0 < s \le 1$.

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Akihiro Fujihara, Toshiya Ohtsuki, Hiroshi Yamamoto. 2006-08-08. On the principle of minimum growth rate in multiplicatively interacting stochastic processes. https://arxiv.org/abs/cond-mat/0608205

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