  Statistics of stochastic processes crucially depends on the imposed boundary
condition. In one spatial dimension, for example, first passage time
distribution in semi-infinite space (one absorbing boundary) is markedly
different from that in a finite interval with two absorbing boundaries. Here we
propose a method, which we call method of filtration, that allows us to
construct the latter from the knowledge of the former only. We argue that our
method is a sort of generalization of the method of image. We also demonstrate
that in terms of the performance, it is complementary to another standard
method based on the eigenfunction expansion solution of the Fokker-Planck
equation.
