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We investigate a stochastic process consisting of a two-dimensional particlewith anisotropic diffusion, mortality rate and a drift velocity, in thepresence of an absorbing boundary. After the particle has encountered theboundary, the process is restarted with updated values of its diffusionconstants 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 giventime and show that, under certain conditions, the eventual hitting probabilitycorresponds to a Bessel distribution. In the context of the man-mosquitoesproblem, the mosquito is able to gradually capture the man, after which themosquito follows a diffusion process with no drift. Our results are comparedthoroughly with Monte Carlo simulations showing excellent agreement.

On the passage properties of the gradual capture of a diffusive particle in the presence of drift