A uniform estimate for the rate of convergence in the multidimensional central limit theorem for homogeneous Markov chains
In this paper a uniform estimate is obtained for the remainder term in the central limit theorem (CLT) for a sequence of random vectors forming a homogeneous Markov chain with arbitrary set of states. The result makes it possible to estimate the rate of convergence in the CLT without assuming the fi...
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| Format: | Article |
| Language: | English |
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Wiley
1996-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171296000634 |
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| _version_ | 1832552162889039872 |
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| author | M. Gharib |
| author_facet | M. Gharib |
| author_sort | M. Gharib |
| collection | DOAJ |
| description | In this paper a uniform estimate is obtained for the remainder term in the central
limit theorem (CLT) for a sequence of random vectors forming a homogeneous Markov chain with
arbitrary set of states. The result makes it possible to estimate the rate of convergence in the CLT
without assuming the finiteness of the absolute third moment of the transition probabilities. Some
consequences are also proved. |
| format | Article |
| id | doaj-art-6ca58b4c613f4f10bbb86560f07247a0 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1996-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-6ca58b4c613f4f10bbb86560f07247a02025-02-03T05:59:28ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251996-01-0119344145010.1155/S0161171296000634A uniform estimate for the rate of convergence in the multidimensional central limit theorem for homogeneous Markov chainsM. Gharib0Mathematics Department, Faculty of Science, Qatar University, QatarIn this paper a uniform estimate is obtained for the remainder term in the central limit theorem (CLT) for a sequence of random vectors forming a homogeneous Markov chain with arbitrary set of states. The result makes it possible to estimate the rate of convergence in the CLT without assuming the finiteness of the absolute third moment of the transition probabilities. Some consequences are also proved.http://dx.doi.org/10.1155/S0161171296000634uniform estimaterate of convergencecentral limit theorem homogeneous Markov chain. |
| spellingShingle | M. Gharib A uniform estimate for the rate of convergence in the multidimensional central limit theorem for homogeneous Markov chains International Journal of Mathematics and Mathematical Sciences uniform estimate rate of convergence central limit theorem homogeneous Markov chain. |
| title | A uniform estimate for the rate of convergence in the multidimensional central limit theorem for homogeneous Markov chains |
| title_full | A uniform estimate for the rate of convergence in the multidimensional central limit theorem for homogeneous Markov chains |
| title_fullStr | A uniform estimate for the rate of convergence in the multidimensional central limit theorem for homogeneous Markov chains |
| title_full_unstemmed | A uniform estimate for the rate of convergence in the multidimensional central limit theorem for homogeneous Markov chains |
| title_short | A uniform estimate for the rate of convergence in the multidimensional central limit theorem for homogeneous Markov chains |
| title_sort | uniform estimate for the rate of convergence in the multidimensional central limit theorem for homogeneous markov chains |
| topic | uniform estimate rate of convergence central limit theorem homogeneous Markov chain. |
| url | http://dx.doi.org/10.1155/S0161171296000634 |
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