Averaged residence times of stochastic motions in bounded domains

TL;DR

This paper develops a new approach to calculate the average residence times of particles undergoing stochastic motions within bounded domains, extending previous work on mean exit times to include various boundary conditions and motion types.

Contribution

It introduces an alternative formulation that computes mean residence times and generalizes results to a broad class of stochastic motions, considering different boundary conditions.

Findings

Derived formulas for mean residence times in bounded domains.

Extended previous models to include internal starting points.

Generalized results for various stochastic motion types.

Abstract

Two years ago, Blanco and Fournier (Blanco S. and Fournier R., Europhys. Lett. 2003) 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. 2004) 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.