THE EQUIVALENCE OF FUNCTIONAL CENTRAL LIMIT THEOREMS FOR COUNTING PROCESSES AND ASSOCIATED PARTIAL SUMS.
Abstract
Let (u sub n, n = or > 1) be a sequence of nonnegative random variables, not necessarily independent or identically distributed, with an associated counting process (N(t), t = or >), defined by N(t) = max (k: u sub 1 + ... + u sub k = or < t), u sub 1 = or < t; N(t) = 0, u sub 1 > t. It is shown that functional central limit theorems (invariance principles) for N(t) are equivalent to corresponding statements for the sequence of partial sums of the u sub n's. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1969
- Accession Number
- AD0690491
Entities
People
- Donald Iglehart
- Ward Whitt
Organizations
- Stanford University