Open Access
2016 On a bound of Hoeffding in the complex case
Mikhail Isaev, Brendan D. McKay
Electron. Commun. Probab. 21: 1-7 (2016). DOI: 10.1214/16-ECP4372


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.


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Mikhail Isaev. Brendan D. McKay. "On a bound of Hoeffding in the complex case." Electron. Commun. Probab. 21 1 - 7, 2016.


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

zbMATH: 1336.60030
MathSciNet: MR3485383
Digital Object Identifier: 10.1214/16-ECP4372

Primary: 33B10 , 60E15

Keywords: bound , complex random variable , diameter , exponential function , Hoeffding

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