Accession Number : AD0764580

Title :   On the Central Limit Theorem for Stationary Processes.

Descriptive Note : Technical rept.,

Corporate Author : STANFORD UNIV CALIF DEPT OF STATISTICS

Personal Author(s) : Heyde,C. C.

Report Date : 12 JUN 1973

Pagination or Media Count : 16

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)

Descriptors :   (*STOCHASTIC PROCESSES, THEOREMS), RANDOM VARIABLES, INVARIANCE, MEASURE THEORY, THEOREMS

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE