MC/CTMC: how can we handle infinite state spaces?

[kevindavisross]

MC takes as an input a transition matrix. How can we define MCs with infinitely many states? For example, how could we define a random walk as an MC? Can we replace the transition matrix with a transition function?

Similarly, CTMCs take a rate matrix as input. Could we replace with a transition rate function when infinitely many states, like in M/M/1 queue?

Should we just have the user set some bounds on likely states and then write code that defines an appropriate transition or rate matrix to input into MC/CTMC? How large of a matrix could Symbulate handle?

Do we already partly have this functionality with PoissonProcess; can we adapt it to general cases?