Random walk models arising in double diffusion and related applications

This thesis is concerned with probabilistic models of double diffusion and related applications, which include a generalization of the gambler's ruin and a problem in queuing theory. Double diffusion theory is applicable to diffusion of ions in metals in the presence of high diffusivity paths. Previous authors have proposed a continuum model, a discrete random walk model and a Master equation model, modelling diffusion in an ideal media but with two families of diffusion paths. For the continuum model a number of mathematical results have been obtained, including solutions of the coupled system of linear parabolic partial differential equations.