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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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##### References:
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