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Periodica Mathematica Hungarica

, Volume 61, Issue 1–2, pp 103–120 | Cite as

An exponential inequality and strong limit theorems for conditional expectations

  • A. ChuprunovEmail author
  • I. Fazekas
Article

Abstract

An exponential inequality for the tail of the conditional expectation of sums of centered independent random variables is obtained. This inequality is applied to prove analogues of the Law of the Iterated Logarithm and the Strong Law of Large Numbers for conditional expectations. As corollaries we obtain certain strong theorems for the generalized allocation scheme and for the nonuniformly distributed allocation scheme.

Key words and phrases

conditional expectation moment Khintchine’s inequality exponential inequality generalized allocation scheme law of the iterated logarithm strong law of large numbers 

Mathematics subject classification number

60F15 

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2010

Authors and Affiliations

  1. 1.Department of Math. Stat. and ProbabilityChebotarev Inst. of Math. and Mechanics Kazan State UniversityKazanRussia
  2. 2.Faculty of InformaticsUniversity of DebrecenDebrecenHungary

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