| Title:
|
A local convergence theorem for partial sums of stochastic adapted sequences (English) |
| Author:
|
Yang, Weiguo |
| Author:
|
Ye, Zhongxing |
| Author:
|
Liu, Wen |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
56 |
| Issue:
|
2 |
| Year:
|
2006 |
| Pages:
|
525-532 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we establish a new local convergence theorem for partial sums of arbitrary stochastic adapted sequences. As corollaries, we generalize some recently obtained results and prove a limit theorem for the entropy density of an arbitrary information source, which is an extension of case of nonhomogeneous Markov chains. (English) |
| Keyword:
|
local convergence theorem |
| Keyword:
|
stochastic adapted sequence |
| Keyword:
|
martingale |
| MSC:
|
60F15 |
| idZBL:
|
Zbl 1164.60338 |
| idMR:
|
MR2291753 |
| . |
| Date available:
|
2009-09-24T11:35:09Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128083 |
| . |
| Reference:
|
[1] P. Algoat, T. Cover: A sandwich proof of the Shannon-McMillan-Breiman theorem.Annals of Probability 16 (1988), 899–909. MR 0929085, 10.1214/aop/1176991794 |
| Reference:
|
[2] W. Liu, J. A. Yan, and W. G. Yang: A limit theorem for partial sums of random variables and its applications.Statistics and Probability Letters 62 (2003), 79–86. MR 1965374, 10.1016/S0167-7152(02)00428-5 |
| Reference:
|
[3] W. Liu: Some limit properties of the multivariate function sequences of discrete random variables.Statistics and Probability Letters 61 (2003), 41–50. Zbl 1016.60034, MR 1950452, 10.1016/S0167-7152(02)00304-8 |
| Reference:
|
[4] W. Liu, W. G. Yang: A limit theorem for the entropy density of nonhomogeneous Markov information source.Statistics and Probability Letters 22 (1995), 295–301. MR 1333187, 10.1016/0167-7152(94)00080-R |
| . |
