Pointwise properties of convergence in probability

Robert M. Burton

Statistics & Probability Letters, 1985, vol. 3, issue 6, 315-316

Abstract: If a sequence of random variables Xn converges to X in probability we know little about the pointwise behavior Xn([omega]). In this note we show that if Xn converges to X quickly enough (for example, like n-[alpha] for [alpha] > 0) then, for almost all [omega], Xn([omega]) converges to X([omega]) outside a set of density zero.

Keywords: convergence; in; probability (search for similar items in EconPapers)
Date: 1985
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