Electronic Communications in Probability

On a bound of Hoeffding in the complex case

Mikhail Isaev and Brendan D. McKay

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It was proved by Hoeffding in 1963 that a real random variable $X$ confined to $[a,b]$ satisfies $\mathbb{E} \, e^{X-\operatorname{\mathbb {E}} X} \le e^{(b-a)^2/8}$. We generalise this to complex random variables.

Article information

Electron. Commun. Probab., Volume 21 (2016), paper no. 14, 7 pp.

Received: 17 June 2015
Accepted: 19 January 2016
First available in Project Euclid: 17 February 2016

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Zentralblatt MATH identifier

Primary: 60E15: Inequalities; stochastic orderings 33B10: Exponential and trigonometric functions

complex random variable exponential function bound diameter Hoeffding

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Isaev, Mikhail; McKay, Brendan D. On a bound of Hoeffding in the complex case. Electron. Commun. Probab. 21 (2016), paper no. 14, 7 pp. doi:10.1214/16-ECP4372. https://projecteuclid.org/euclid.ecp/1455717136

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