The residence time of a Brownian particle within a spatial domain is the total time it spends within this domain. It is shown that the residence time distribution can be calculated from the survival probability for a constant trapping rate inside the domain. This isomorphism is exploited to derive explicit relations for the distribution and its moments for a three-dimensional spherical domain. Results are verified by a Brownian dynamics simulation.
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Berezhkovskii et al. (1998) studied this question.
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