After reviewing the wide field of application of stochastic processes in Chemical Engineering, with specific attention to particulate processes, the definition of a Markov chain is given and commented upon using an example. Batch grinding processes are then analysed from this point of view, emphasizing the link that exists between both stochastic and deterministic (based on population balance) approaches. Breakage and selection functions appear to be clearly linked to the transition probabilities of a Markov chain via the definition of a time interval characteristic of the grinding process. This provides a physical significance for the time interval. An identical analysis is made for continuous grinding processes which underlines again the similarity between both approaches. These concepts are illustrated by the use of experimental grinding data obtained in a stirred bead mill which shows the high degree of fit of the Markov chain model for both continuous and batch experiments.