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\(L_p\)-version of the Dubins-Savage inequality and some exponential inequalities. (English) Zbl 1166.60016
Summary: The Dubins-Savage inequality is generalized by using the \(p\)th \((1<p\leq 2)\) conditional moment of the martingale differences. This inequality is further extended under suitable conditions when \(p>2\). Another martingale inequality due to Freedman is also generalized when \(0<p\leq 2\). Implications of these inequalities for strong convergence are discussed. Some general exponential inequalities are also given for martingales (supermartingales) under suitable conditions.

MSC:
60E15 Inequalities; stochastic orderings
60G42 Martingales with discrete parameter
60F15 Strong limit theorems
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