## Electronic Communications in Probability

### On a bound of Hoeffding in the complex case

#### Abstract

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

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

Dates
Accepted: 19 January 2016
First available in Project Euclid: 17 February 2016

https://projecteuclid.org/euclid.ecp/1455717136

Digital Object Identifier
doi:10.1214/16-ECP4372

Mathematical Reviews number (MathSciNet)
MR3485383

Zentralblatt MATH identifier
1336.60030

#### Citation

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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