Feller chains and random functions - Kazakevičius, Vytautas (Lietuvos matematikos rinkinys, 2015)
We prove that each Feller transition probability is the one-dimensional distribution of some stochastically continuous random function. We also introduce the notion of a regular random function and show, on one hand, that every random function has a regular modification, and on the other hand, that the composition of independent regular stochastically continuous random functions is stochastically continuous as well.