Optimization of the residence time of a Brownian particle in a spherical subdomain

In this communication, we show that the residence time of a Brownian particle, defined as the cumulative time spent in a given region of space, can be optimized as a function of the diffusion coefficient. We discuss the relevance of this effect to several schematic experimental situations classified in nature-random or deterministic-both of the observation time and of the starting position of the Brownian particle. (C) 2009 American Institute of Physics. [doi: 10.1063/1.3264122]