First-passage quantities of Brownian motion in a bounded domain with multiple targets: a unified approach

In this paper, we introduce a general computation method to systematically determine the mean first-passage time (MFPT), the global mean first-passage time (GMFPT) and splitting probabilities for a continuous Brownian motion in a confined 2D or 3D domain with multiple absorbing targets in the bulk or on the boundary. This method is applied to spherically symmetric domains in the limit of small-sized targets and asymptotic expansions of the MPFT, GMFPT and splitting probabilities are obtained in four distinct cases: 3D domains with targets in the bulk, 3D domains with targets on the boundary, 2D domains with targets on the bulk and 2D domains with targets on the boundary. This approach gives a unified description of existing exact results which were obtained using specific technics, and also yields new results, in particular for N targets splitting probabilities.