Sharp Bounds on The LP Norm of a Randomly Stopped Multilinear form with an Application to Wald’S Equation

doi:https://doi.org/10.1007/978-1-4612-0367-4_4

Sharp Bounds on The LP Norm of a Randomly Stopped Multilinear form with an Application to Wald’S Equation

Víctor Peña-1992-01-01-Birkhäuser Boston eBooks

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TL;DRAbstract

This paper presents a sharp bound on the L p norm (1 ≤ p ≤ 2) of a randomly stopped multilinear form of i.i.d. mean zero random variables. As a corollary we obtain optimal conditions for Wald’s equation for this multilinear form to hold. The bound obtained generalizes earlier work of (1991) and (1988). The techniques used include decoupling inequalities and the argument of subsequences.

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This paper presents a sharp bound on the L p norm (1 ≤ p ≤ 2) of a randomly stopped multilinear form of i.i.d. mean zero random variables. As a corollary we obtain optimal conditions for Wald’s equation for this multilinear form to hold. The bound obtained generalizes earlier work of (1991) and (1988). The techniques used include decoupling inequalities and the argument of subsequences.

Keywords

Multilinear mapCorollaryMathematicsNorm (philosophy)Decoupling (probability)Upper and lower boundsApplied mathematicsPure mathematics

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