ON DEGENERATE SUMS OF m-DEPENDENT VARIABLES
2015 (English)In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 52, no 4, 1146-1155 p.Article in journal (Refereed) PublishedText
It is well known that the central limit theorem holds for partial sums of a stationary sequence (X-i) of m-dependent random variables with finite variance; however, the limit may be degenerate with variance 0 even if var(X-i) not equal 0. We show that this happens only in the case when X-i - EXi = Y-i - Y-i for an (m - 1)-dependent stationary sequence (Y-i) with finite variance (a result implicit in earlier results), and give a version for block factors. This yields a simple criterion that is a sufficient condition for the limit not to be degenerate. Two applications to subtree counts in random trees are given.
Place, publisher, year, edition, pages
2015. Vol. 52, no 4, 1146-1155 p.
m-dependent, stationary sequence, block factor, random tree
IdentifiersURN: urn:nbn:se:uu:diva-277888ISI: 000368467600016OAI: oai:DiVA.org:uu-277888DiVA: diva2:907002
FunderKnut and Alice Wallenberg Foundation