Basics of stochastic processes

Sometimes it is necessary to consider random variables or vectors that depend on time. Definition 2.1 A sequence of random variables ξt, t=0, 1, 2,…, is said to be a discrete

time stochastic (or random) process. Definition 2.2 Let be given. A mapping ξ:[0,T]×Ω→R is said to be a

continuous time stochastic (random) process if ξ(t,ω) is a random variable for a.e. (almost every) t.