STOCHASTIC PROCESS

in probability theory, a family of random variables indexed by some other set and having the property that for each finite subset of the index set, the collection of random variables thus indexed has a joint probability distribution; it is one of the most general objects of study in probability. These distributions are compatible with each other, a property that ensures that there exists some probability space and some family of random variables defined on the space that realizes the original stochastic process. Examples of stochastic processes include Markov processes, Poisson processes, and time series, with the index family originally thought of as referring to time. This indexing is either discrete or continuous, the interest being in the nature of changes of the variables with respect to time.