Volume 70, Number 1, April 2005
|Page(s)||42 - 48|
|Published online||09 March 2005|
Averaged residence times of stochastic motions in bounded domains
Laboratoire de Physique Théorique des Liquides (CNRS UMR 7600) Université Pierre et Marie Curie - 4 place Jussieu, case courrier 121, 75255 Paris Cedex 05, France
2 Institut Curie - 26 rue d'Ulm, 75248 Paris Cedex 05, France
Corresponding author: firstname.lastname@example.org
Accepted: 10 February 2005
Two years ago, Blanco and Fournier (Blanco S. and Fournier R., Europhys. Lett. 61 (2003) 168) calculated the mean first exit time of a domain of a particle undergoing a randomly reoriented ballistic motion which starts from the boundary. They showed that it is simply related to the ratio of the volume's domain over its surface. This work was extended by Mazzolo (Mazzolo A., Europhys. Lett. 68 (2004) 350), who studied the case of trajectories which start inside the volume. In this letter, we propose an alternative formulation of the problem which allows us to calculate not only the mean exit time, but also the mean residence time inside a sub-domain. The cases of any combinations of reflecting and absorbing boundary conditions are considered. Lastly, we generalize our results for a wide class of stochastic motions.
PACS: 05.40.Fb – Random walks and Levy flights / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 02.50.-r – Probability theory, stochastic processes, and statistics
© EDP Sciences, 2005
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.