A probabilistic version of Rosenthal's inequality

S. V. Astashkin; K. E. Tikhomirov

doi:10.1090/S0002-9939-2013-11713-2

A probabilistic version of Rosenthal's inequality

S. V. Astashkin, K. E. Tikhomirov

Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We prove some probabilistic relations between sums of independent random variables and the corresponding disjoint sums, which strengthen the well-known Rosenthal inequality and its generalizations. As a consequence we extend the inequalities proved earlier by Montgomery-Smith and Junge for rearrangement invariant spaces to the quasi-normed case.

Original language	English (US)
Pages (from-to)	3539-3547
Number of pages	9
Journal	Proceedings of the American Mathematical Society
Volume	141
Issue number	10
DOIs	https://doi.org/10.1090/S0002-9939-2013-11713-2
State	Published - 2013

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

Keywords

Independent random variables
Quasi-normed symmetric sequence space
Rearrangement invariant space
Rosenthal's inequality

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10.1090/S0002-9939-2013-11713-2

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title = "A probabilistic version of Rosenthal's inequality",

abstract = "We prove some probabilistic relations between sums of independent random variables and the corresponding disjoint sums, which strengthen the well-known Rosenthal inequality and its generalizations. As a consequence we extend the inequalities proved earlier by Montgomery-Smith and Junge for rearrangement invariant spaces to the quasi-normed case.",

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AU - Astashkin, S. V.

AU - Tikhomirov, K. E.

PY - 2013

Y1 - 2013

N2 - We prove some probabilistic relations between sums of independent random variables and the corresponding disjoint sums, which strengthen the well-known Rosenthal inequality and its generalizations. As a consequence we extend the inequalities proved earlier by Montgomery-Smith and Junge for rearrangement invariant spaces to the quasi-normed case.

AB - We prove some probabilistic relations between sums of independent random variables and the corresponding disjoint sums, which strengthen the well-known Rosenthal inequality and its generalizations. As a consequence we extend the inequalities proved earlier by Montgomery-Smith and Junge for rearrangement invariant spaces to the quasi-normed case.

KW - Independent random variables

KW - Quasi-normed symmetric sequence space

KW - Rearrangement invariant space

KW - Rosenthal's inequality

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JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

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ER -

A probabilistic version of Rosenthal's inequality

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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