Laws of large numbers
著者
書誌事項
Laws of large numbers
Narosa, c2012
- : hbk.
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内容説明・目次
内容説明
Laws of Large Numbers contains the usual laws of large numbers together with the recent ones derived in unified and elementary approaches. Most of these results are valid for dependent and possibly non-identical sequence of random variables. These are established under much greater generalities with methods drastically simpler than the standard ones available in current text-books.
Using the uniform Integrability type conditions, the monograph supplements the strong laws of large numbers by proving Lp-convergence of the sample mean to its expectations.
目次
Some Classical Laws of Large Numbers: Chebyshev's Inequality and its Applications
Borel-Cantelli Lemmas
Some Notions of Stochastic Convergence
Uniform Integrability
Some Well-known Laws of Large Numbers
Some Recent Laws of Large Numbers: Some Recent L1 - LLNs
Some Recent SLLNs
Some Recent Lp - LLNs
Some Further Results on SLLN: Method of Subsequences
Marcinkiewicz-Zygmund SLLN
Mixingales
SLLN for the Weighted Averages
Extensions of an Inequality of Kolmogorov
Miscellaneous Results
Appendixes
Bibliography
Index.
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