  We investigate a stochastic process consisting of a two-dimensional particle
with anisotropic diffusion, mortality rate and a drift velocity, in the
presence of an absorbing boundary. After the particle has encountered the
boundary, the process is restarted with updated values of its diffusion
constants and drift velocity. We then derive the joint probability that, after
$M$ encounters, the particle is absorbed at a point of the boundary at a given
time and show that, under certain conditions, the eventual hitting probability
corresponds to a Bessel distribution. In the context of the man-mosquitoes
problem, the mosquito is able to gradually capture the man, after which the
mosquito follows a diffusion process with no drift. Our results are compared
thoroughly with Monte Carlo simulations showing excellent agreement.
