Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1156538 | Stochastic Processes and their Applications | 2014 | 13 Pages |
Abstract
In 1983, N. Herrndorf proved that for a ϕϕ-mixing sequence satisfying the central limit theorem and lim infn→∞σn2/n>0, the weak invariance principle takes place. The question whether for strictly stationary sequences with finite second moments and a weaker type (αα, ββ, ρρ) of mixing the central limit theorem implies the weak invariance principle remained open.We construct a strictly stationary ββ-mixing sequence with finite moments of any order and linear variance for which the central limit theorem takes place but not the weak invariance principle.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Davide Giraudo, Dalibor Volný,