Stochastic Process

A stochastic process is a collection of random variables defined on a common probability space, taking values from the same mathematical space known as the state space and indexed by some mathematical set usually N or [0,∞) known as an index set. When thought in terms of time, if the index set of a stochastic process has a finite or countable number of elements, such as a finite set of numbers or the natural numbers, then the stochastic process is said to be a discrete-time stochastic process. If the index set is some interval of the real line, then it is said to be a continuous-time stochastic process.