Stationary (Strict Sense) Random Sequences and Ergodic Theory

Abstract

Let (Ω ℱ P) be a probability space and $\xi = \left( {{\xi _1},{\xi _2},...} \right)$ a sequence of random variables or, as we say, a random sequence. Let θ _k ξ denote the sequence $\left( {{\xi _{k + 1}},{\xi _{k + 2}},...} \right)$.