On the Central Limit Theorem and Iterated Logarithm Law for Stationary Processes.

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Abstract:

Invariance principles are given for both the central limit theorem and iterated logarithm law for a wide class of stationary processes. The results are derived from corresponding results for martingales with stationary ergodic increments. This is accomplished via a representation for the stationary process in terms of stationary martingale differences plus other terms whose sum telescopes and disappears under suitable norming. An application is given to show how previously known results for stationary uniformly mixing processes can be improved. Author

Author(s):
Heyde, C. C.
Author Organization(s):
STANFORD UNIV CALIF DEPT OF STATISTICS
Descriptive Note:
Technical rept.,
Pagination:
0016

Security Markings

DOCUMENT & CONTEXTUAL SUMMARY

Distribution:
Approved For Public Release

RECORD

Collection: TR
Identifying Numbers
Report Number(s):
TR-76
Contract/Grant Number(s):
N00014-67-A-0112-0051
Project Number(s):
NR-042-993
 Subject Terms
Communities of Interest:
Materials and Manufacturing Processes
Descriptor(s):
(*STOCHASTIC PROCESSES, INVARIANCE), RANDOM VARIABLES, MEASURE THEORY, THEOREMS, HILBERT SPACE
Field(s)/Group(s):
Statistics and Probability
Keyword(s):
LAW OF THE ITERATED LOGARITHM, LOGARITHM FUNCTIONS, MARTINGALES, *CENTRAL LIMIT THEOREM, *STATIONARY PROCESSES, ERGODIC PROCESSES
Report Date:
1973 Mar 26