The aim of a particle transport theory in stochastic media is to describe the ensemble-averaged and higher moments of the flux by a relatively small set of deterministic equations. These equations based on the classical transport equations describe the transport of particles when the properties of the background material (host medium), as functions of space and time, are only known in a statistical sense. The goal of this work is to find a simple set of equations to describe the mean flux of particles, in this case neutrons. Chapter 1 indicates in which cases this new theory called stochastic transport may be used. This Chapter describes particularly the problem of criticality calculation of a molten Corium, composed of a mixture of all possible reactor elements, spread on a core catcher. The flooding of the melt with water produces a substantial fragmentation with the appearance of water cracks which sizes and distributions are random. Chapter 2 describes the bases of the stochastic transport problem. This description consists of an infinite hierarchy of equations which can not be used to directly solve practical problems. So, it is necessary to truncate this hierarchy by an approximate closure. This approximation can be validated only with benchmark results. Chapter 3 displays complete benchmark results for the particle transmission problem through a system with a finite thickness. This system describes a background media composed of two randomly mixed materials following an equilibrium alternating renewal process. The results given are the coefficients of reflection and transmission and three different types of ensemble-averaged flux for all interior location points. These results confirm previous evidence that different statistics yield different results and that mean and variance are the parameters of the statistical distributions that have the largest influence on the transport problem. In Chapter 4 we describe the closure schemes used to obtain models for the transport problem in renewal media. The predictions of these models are compared with the above benchmark results. The best of them solve the transmission problem with an accuracy of 5%. Finally, Chapter 5 applies the best and simplest model, the constrained model, to a multigroup formalism in an infinite statistical medium. This model is used to homogenize the fragmented Corium spread on the concrete of a core catcher and cooled by water injection from the top. The homogenization with the stochastic theory is compared to the standard volume homogenization. The results indicate which statistical parameters are necessary for an accurate prediction of the system reactivity and what amount of errors implies the uncertainty of these statistical parameters.