 
Summary: Residence time distribution of a Brownian particle
Alexander M. Berezhkovskii,* Veaceslav Zaloj,
and Noam Agmon
The Fritz Haber Research Center, Department of Physical Chemistry, The Hebrew University, Jerusalem 91904, Israel
Received 18 June 1997
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 threedimensional spherical domain. Results are verified by a Brownian
dynamics simulation. S1063651X 98 085043
PACS number s : 05.40. j, 82.20.Fd, 82.20.Wt
I. INTRODUCTION
Consider a particle which spends all of its lifetime within
a prescribed spatial domain. The particle disappears either
from the interior of the domain or from its boundary. When
the motion of the particle is governed by probabilistic laws,
such as, for example, random walk or Brownian motion, one
can speak about the particle mean lifetime, the first moment
of its lifetime distribution 1,2 . The mean lifetime is of fun
damental importance for diffusion influenced reactions, as it
