| Issue |
EPL
Volume 109, Number 4, February 2015
|
|
|---|---|---|
| Article Number | 40015 | |
| Number of page(s) | 5 | |
| Section | General | |
| DOI | https://doi.org/10.1209/0295-5075/109/40015 | |
| Published online | 05 March 2015 | |
From Markovian to non-Markovian persistence exponents
SAMM (EA 4543), Université Paris-1 Panthéon-Sorbonne, Centre Pierre Mendès-France - 90 rue de Tolbiac, 75013 Paris, France
Received: 30 December 2014
Accepted: 11 February 2015
We establish an exact formula relating the survival probability for certain Lévy flights (viz. asymmetric α-stable processes where 
) with the survival probability for the order statistics of the running maxima of two independent Brownian particles. This formula allows us to show that the persistence exponent δ in the latter non-Markovian case is simply related to the persistence exponent θ in the former Markovian case via: 
. Thus, our formula reveals a link between two recently explored families of anomalous exponents: one exhibiting continuous deviations from Sparre-Andersen universality in a Markovian context, and one describing the slow kinetics of the non-Markovian process corresponding to the difference between two independent Brownian maxima.
PACS: 05.40.Fb – Random walks and Levy flights / 05.40.Jc – Brownian motion / 02.50.Ey – Stochastic processes
© EPLA, 2015
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