On the Central Limit Theorem for Stationary Processes.
Abstract
A central limit theorem is given with application to a wide class of processes ((S sub M) = summation from i = 1 to n of (X sub i)) with stationary ergodic increments (X sub i) having zero mean and finite variance and such that lim as N approaches infinity (N sup -1) E (S sup 2, sub n) = (Sigma squared), 0 < (Sigma squared) < infinity. The results are derived from the central limit theorem for martingales with stationary ergodic increments via the construction of a martingale whose differences have variance (Sigma squared) and which approximates (S sub n). An application is given to show how previously known central limit results for stationary uniformly mixing processes can be improved. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 12, 1973
- Accession Number
- AD0764580
Entities
People
- C. C. Heyde
Organizations
- Stanford University