Some Weak and Strong Laws of Large Numbers for D(0,1) - Valued Random Variables.

reportActive / Technical Report | Accession Number: ADA144845 | Open PDF

Abstract:

Pointwise Weak Law of Large Numbers and Weak Law of Large Numbers in the norm topology of D0,1 are shown to be equivalent under uniform convex tightness and uniform integrability conditions for weighted sums of a sequence of random elements in D0,1. Uniform convex tightness and uniform integrability conditions are jointly characterized. Marcinkiewicz-Zygmund-Kolmogorovs and Brunk-Chungs Strong Laws of Large Numbers are derived in the setting of D0,1 - space under uniform convex tightness and uniform integrability conditions. Equivalence of pointwise convergence, convergence in the Skorokhod topology and convergence in the norm topology for sequences in D0,1 is studied. Author

Author(s):
Wang, X. C. ; Rao, M. B.
Author Organization(s):
PITTSBURGH UNIV PA CENTER FOR MULTIVARIATE ANALYSIS
Descriptive Note:
Technical rept.,
Supplementary Note:
DOI: 10.21236/ADA144845
Pagination:
0045

Security Markings

DOCUMENT & CONTEXTUAL SUMMARY

Distribution:
Approved For Public Release

RECORD

Collection: TR
Identifying Numbers
Report Number(s):
TR-84-36, AFOSR-TR-84-0714
Contract/Grant Number(s):
F49620-82-K-0001
Task Number(s):
A5
Project Number(s):
2304
Monitor Series:
TR-84-0714
 Subject Terms
Joint Capability Areas:
JCA_6.1_Information Transport; JCA_6_Net Centric; JCA_5_Command and Control; JCA_1.2_Force Preparation; JCA_1_Force Support; JCA_1.2.3_Educating; JCA_5.3_Planning; JCA_1.2.5_Lessons Learned
Modernization Areas:
Fully Networked C3
Communities of Interest:
C4I
Descriptor(s):
*RANDOM VARIABLES, *CONVERGENCE, *NUMBERS, STOCHASTIC PROCESSES, TOPOLOGY, TIGHTNESS, THEOREMS, CONVEX BODIES, BANACH SPACE
Field(s)/Group(s):
Statistics and Probability
Keyword(s):
WUAFOSR2304A5, PE61102F
Report Date:
1984 Jul 01