Strong Approximation

Abstract

Larger parts of this book are centered upon mixed empirical processes that concern random samples

$${X_1},{X_2},...,{X_\zeta }$$

where X₁, X₂, X₃, ... are independent, identically distributed (i.i.d.) random elements in the basic space S, and ζ is a random sample size that is independent of the X _i . The present chapter will provide a detailed discussion of special mixed empirical processes, namely, of binomial processes and Poisson processes with finite intensity measures. In these cases the random sample size ζ is a binomial and, respectively, a Poisson random variable (r.v.). Further examples of mixed empirical processes and a thorough treatment of that subject may be found in Section 2.2.