Article contents
On degenerate sums of m-dependent variables
Published online by Cambridge University Press: 30 March 2016
Abstract
It is well known that the central limit theorem holds for partial sums of a stationary sequence (Xi) of m-dependent random variables with finite variance; however, the limit may be degenerate with variance 0 even if var(Xi) ≠ 0. We show that this happens only in the case when Xi – EXi = Yi – Yi–1 for an (m − 1)-dependent stationary sequence (Yi) 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.
MSC classification
- Type
- Research Papers
- Information
- Copyright
- Copyright © Applied Probability Trust 2015
References
- 6
- Cited by