An exponential inequality and strong limit theorems for conditional expectations
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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 phrasesconditional expectation moment Khintchine’s inequality exponential inequality generalized allocation scheme law of the iterated logarithm strong law of large numbers
Mathematics subject classification number60F15
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