Abstract
Let a particle start at some point in the unit interval I := [0, 1]
and undergo Brownian motion in I until it hits one of the end points. At
this instant the particle stays put for a finite holding time with an
exponential distribution and then jumps back to a point inside I with a
probability density μ0 or μ1 parametrized by the boundary point it was
from. The process starts afresh. The same evolution repeats
independently each time. Many probabilistic aspects of this diffusion
process are investigated in the paper [10]. The authors in the cited
paper call this process diffusion with holding and jumping (DHJ). Our
simple aim in this paper is to analyze the eigenvalues of a nonlocal
boundary problem arising from this process.