Abstract of the poster "Residence times and other functionals of reflected Brownian motion"
We propose a general solution to the problem of finding the
probability distribution of residence times of a Brownian particle
confined by reflecting boundaries. Its Fourier transform
(characteristic function) and Laplace transform (survival probability)
are obtained in a compact matrix form involving the Laplace operator
eigenbasis. When the eigenbasis (or its part) is known, the numerical
computation of the residence time distributions is straightforward and
very accurate. The present approach can also be applied to
investigate other functionals of the reflected Brownian motion
describing, in particular, restricted diffusion in an external field
or potential (e.g., nuclei diffusing in an inhomogeneous magnetic
field).
Keywords: restricted diffusion, residence time, Laplace operator eigenfunctions