A critique of the stochastic transition matrix formalism

The Stochastic Transition Matrix (STM) formalism has been introduced by Akcasu to compute the ensemble average flux of bimaterial stochastic density statistics with deterministic sources. The method uses an integral flux representation based on a stochastic propagator and as boundary conditions the entering and exiting fluxes at the left of a finite slab. In this paper we generalize the STM formalism to the energy-dependent continuous transport equation, analyze and discuss basic issues of the formalism and compare it to the classical Levermore-Pomranig model and to reference calculations for simplified rod problems. We also extend the formalism in two different ways to consistently compute the ensemble and the material averages flux.