  The sampling of the configuration space in diffusion Monte Carlo (DMC) is
done using walkers moving randomly. In a previous work on the Hubbard model
[\href{https://doi.org/10.1103/PhysRevB.60.2299}{Assaraf et al.~Phys.~Rev.~B
\textbf{60}, 2299 (1999)}], it was shown that the probability for a walker to
stay a certain amount of time in the same state obeys a Poisson law and that
the on-state dynamics can be integrated out exactly, leading to an effective
dynamics connecting only different states. Here, we extend this idea to the
general case of a walker trapped within domains of arbitrary shape and size.
The equations of the resulting effective stochastic dynamics are derived. The
larger the average (trapping) time spent by the walker within the domains, the
greater the reduction in statistical fluctuations. A numerical application to
the Hubbard model is presented. Although this work presents the method for
finite linear spaces, it can be generalized without fundamental difficulties to
continuous configuration spaces.
