Stochastic Independence

Abstract

The first six sections of this chapter describe the measure-theoretic foundation for ‘stochastic independence’: products of probability spaces. After giving the basic definitions, we prove the existence of ‘product measure’ and also give an important result concerning integration with respect to product measure (the Fubini Theorem). Important relations among expectations, independence, and densities are described. The last three sections of the chapter do not depend on each other. The first treats the asymptotic behavior of sequences of independent identically distributed random variables. The second concerns ‘order statistics’ of finite sequences of such random variables. The last introduces some new distributions.