Power laws from randomly sampled continuous-time random walks

Giancarlo Mosetti; Giancarlo Jug; Enrico Scalas

doi:10.1016/j.physa.2006.08.065

Power laws from randomly sampled continuous-time random walks

Giancarlo Mosetti
, Giancarlo Jug
, Enrico Scalas

Research output: Contribution to journal › Article › peer-review

Abstract

It has been shown by Reed that random-sampling a Wiener process x (t) at times T chosen out of an exponential distribution gives rise to power laws in the distribution P (x (T)) ∼ x (T)^{- β}. We show, both theoretically and numerically, that this power-law behaviour also follows by random-sampling Lévy flights (as continuous-time random walks), having Fourier distribution over(w, ^) (k) = e^{- | k |α}, with the exponent β = α.

Original language	English
Pages (from-to)	233-238
Number of pages	6
Journal	Physica A: Statistical Mechanics and its Applications
Volume	375
Issue number	1
DOIs	https://doi.org/10.1016/j.physa.2006.08.065
Publication status	Published - 15 Feb 2007
Externally published	Yes

Keywords

Continuous-time random walks
Population dynamics
Power laws

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10.1016/j.physa.2006.08.065

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title = "Power laws from randomly sampled continuous-time random walks",

abstract = "It has been shown by Reed that random-sampling a Wiener process x (t) at times T chosen out of an exponential distribution gives rise to power laws in the distribution P (x (T)) ∼ x (T)- β. We show, both theoretically and numerically, that this power-law behaviour also follows by random-sampling L{\'e}vy flights (as continuous-time random walks), having Fourier distribution over(w, \textasciicircum{}) (k) = e- | k |α, with the exponent β = α.",

keywords = "Continuous-time random walks, Population dynamics, Power laws",

author = "Giancarlo Mosetti and Giancarlo Jug and Enrico Scalas",

note = "Funding Information: We are grateful to G. Bottazzi and G. Yaari for useful discussions. E. S. has been partially supported by the Italian MIUR project {\textquotedblleft}Dinamica di altissima frequenza nei mercati finanziari{\textquotedblright}.",

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AU - Mosetti, Giancarlo

AU - Jug, Giancarlo

AU - Scalas, Enrico

N1 - Funding Information: We are grateful to G. Bottazzi and G. Yaari for useful discussions. E. S. has been partially supported by the Italian MIUR project “Dinamica di altissima frequenza nei mercati finanziari”.

PY - 2007/2/15

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N2 - It has been shown by Reed that random-sampling a Wiener process x (t) at times T chosen out of an exponential distribution gives rise to power laws in the distribution P (x (T)) ∼ x (T)- β. We show, both theoretically and numerically, that this power-law behaviour also follows by random-sampling Lévy flights (as continuous-time random walks), having Fourier distribution over(w, ^) (k) = e- | k |α, with the exponent β = α.

AB - It has been shown by Reed that random-sampling a Wiener process x (t) at times T chosen out of an exponential distribution gives rise to power laws in the distribution P (x (T)) ∼ x (T)- β. We show, both theoretically and numerically, that this power-law behaviour also follows by random-sampling Lévy flights (as continuous-time random walks), having Fourier distribution over(w, ^) (k) = e- | k |α, with the exponent β = α.

KW - Continuous-time random walks

KW - Population dynamics

KW - Power laws

UR - https://www.scopus.com/pages/publications/34548489081

U2 - 10.1016/j.physa.2006.08.065

DO - 10.1016/j.physa.2006.08.065

M3 - Article

SN - 0378-4371

VL - 375

SP - 233

EP - 238

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

IS - 1

ER -

Power laws from randomly sampled continuous-time random walks

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