E-ISBN: Publication Year: 2012
Binding: Hard Back Dimension: 160mm x 240mm Weight: 590
About the book
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.
Table of Contents
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.