Europhys. Lett.
Volume 70, Number 1, April 2005
Page(s) 42 - 48
Section General
Published online 09 March 2005
Europhys. Lett., 70 (1), pp. 42-48 (2005)
DOI: 10.1209/epl/i2005-10001-y

Averaged residence times of stochastic motions in bounded domains

O. Bénichou1, M. Coppey1, M. Moreau1, P. H. Suet1 and R. Voituriez2

1  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

received 17 January 2005; accepted in final form 10 February 2005
published online 9 March 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.

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.

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