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

Risultato della ricerca: Contributo su rivista › Articolo in rivista › 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.

Lingua originale	Inglese
pagine (da-a)	233-238
Numero di pagine	6
Rivista	Physica A: Statistical Mechanics and its Applications
Volume	375
Numero di pubblicazione	1
DOI	https://doi.org/10.1016/j.physa.2006.08.065
Stato di pubblicazione	Pubblicato - 15 feb 2007
Pubblicato esternamente	Sì

Accesso al documento

10.1016/j.physa.2006.08.065

Altri file e collegamenti

Link to publication in Scopus

Cita questo

@article{1d59d248e731421098b82700350a0acc,

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 “Dinamica di altissima frequenza nei mercati finanziari”.",

year = "2007",

month = feb,

day = "15",

doi = "10.1016/j.physa.2006.08.065",

language = "English",

volume = "375",

pages = "233--238",

journal = "Physica A: Statistical Mechanics and its Applications",

issn = "0378-4371",

publisher = "Elsevier BV",

number = "1",

}

TY - JOUR

T1 - Power laws from randomly sampled continuous-time random walks

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

Y1 - 2007/2/15

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

Abstract

Accesso al documento

Altri file e collegamenti

Fingerprint

Cita questo