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 - http://www.scopus.com/inward/record.url?scp=34548489081&partnerID=8YFLogxK
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 -