Can we characterize a stochastic process over space as opposed to stochastic process over time?

Question

Strictly speaking, a stochastic process can characterize a collection of random variables whose index is not time-related. Please, are there examples in the literature where this has been considered? Otherwise, should we refer to those processes as random fields as opposed to stochastic processes, reserving the term "stochastic process" for the case wherein time is involved? I'm particularly curious about the case wherein there is a process over space as opposed to process over time.