A strong limit theorem for functions of continuous random variables and an extension of the Shannon-McMillan theorem.
Li, Gaorong, Chen, Shuang, Feng, Sanying (2008)
Journal of Applied Mathematics
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Displaying similar documents to “A local convergence theorem for partial sums of stochastic adapted sequences”
A strong limit theorem for functions of continuous random variables and an extension of the Shannon-McMillan theorem.
A class of strong limit theorems for countable nonhomogeneous Markov chains on the generalized gambling system
Kangkang Wang (2009)
Czechoslovak Mathematical Journal
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In this paper, we study the limit properties of countable nonhomogeneous Markov chains in the generalized gambling system by means of constructing compatible distributions and martingales. By allowing random selection functions to take values in arbitrary intervals, the concept of random selection is generalized. As corollaries, some strong limit theorems and the asymptotic equipartition property (AEP) theorems for countable nonhomogeneous Markov chains in the generalized gambling system...
A variant of Jensen's inequality.
Mercer, A.McD. (2003)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
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Stochastic analysis of Bernoulli processes.
Privault, Nicolas (2008)
Probability Surveys [electronic only]
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A refinement of various mean inequalities.
Hara, Takuya, Uchiyama, Mitsuru, Takahasi, Sin-Ei (1998)
Journal of Inequalities and Applications [electronic only]
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Convergence theorems for partial sums of arbitrary stochastic sequences.
Wang, Xiaosheng, Guo, Haiying (2010)
Journal of Inequalities and Applications [electronic only]
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On strong law of large numbers for dependent random variables.
Wang, Zhongzhi (2011)
Journal of Inequalities and Applications [electronic only]
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Thin sequences in the corona of H ∞
Dimcho Stankov, Tzonio Tzonev (2013)
Open Mathematics
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In this paper we consider several conditions for sequences of points in M(H ∞) and establish relations between them. We show that every interpolating sequence for QA of nontrivial points in the corona of H ∞ is a thin sequence for H ∞, which satisfies an additional topological condition. The discrete sequences in the Shilov boundary of H ∞ necessarily satisfy the same condition.