  Traditional Monte Carlo methods for particle transport utilize source
iteration to express the solution, the flux density, of the transport equation
as a Neumann series. Our contribution is to show that the particle paths
simulated within source iteration are associated with the adjoint flux density
and the adjoint particle paths are associated with the flux density. We make
our assertion rigorous through the use of stochastic calculus by representing
the particle path used in source iteration as a solution to a stochastic
differential equation (SDE). The solution to the adjoint Boltzmann equation is
then expressed in terms of the same SDE and the solution to the Boltzmann
equation is expressed in terms of the SDE associated with the adjoint particle
process. An important consequence is that the particle paths used within source
iteration simultaneously provide Monte Carlo approximations of the flux density
and adjoint flux density. Monte Carlo simulations are presented to support the
simultaneous use of the particle paths.
