Abstract
This chapter focuses on stationary sequences of random variables by considering some examples of stochastic processes. Ergodic theory provides a vehicle for the study of stationary sequences; the basic “pointwise ergodic theorem” is a generalization of the strong law of large numbers. The starting point for ergodic theory is the notion of a measure-preserving transformation. The pointwise ergodic theorem is applied to prove a basic result of information theory. The chapter discusses the development of the Shannon-McMillan theorem.
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