Volume 92, Number 5, December 2010
|Number of page(s)
|04 January 2011
First passage time distribution of stationary Markovian processes
Dipartimento di Fisica e Tecnologie Relative, Università di Palermo - V.le delle Scienze Ed. 18, 90128 Palermo, Italy, EU
Accepted: 22 November 2010
We investigate how the correlation properties of a stationary Markovian stochastic process affect its First Passage Time Distribution (FPTD). With explicit examples, in this paper we show that the tail of the first passage time distribution crucially depends on the correlation properties of the process and it is independent of its stationary distribution. When the process includes an infinite set of time-scales bounded from above, the FPTD shows tails modulated by some exponential decay. In the case when the process is power-law correlated the FPTD shows power-law tails 1/tν and therefore the moments ⟨tn⟩ of the FPTD are finite only when n < ν−1. The existence of an infinite and unbounded set of time-scales is a necessary but not sufficient condition in order to observe power-law tails in the FPTD. Finally, we give a general result connecting the FPTD of an additive stochastic processes x(t) to the FPTD of a generic process y(t) related by a coordinate transformation y = f(x) to the first one.
PACS: 02.50.Ey – Stochastic processes / 05.10.Gg – Stochastic analysis methods (Fokker-Planck, Langevin, etc.) / 02.50.Ga – Markov processes
© EPLA, 2010
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.