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Converse Jensen inequality. (English) Zbl 1180.60017

Summary: We use Skorokhod’s embedding theorem to give a new proof of a converse to Jensen’s inequality.

MSC:

60E15 Inequalities; stochastic orderings
60J65 Brownian motion
26A51 Convexity of real functions in one variable, generalizations
26D15 Inequalities for sums, series and integrals
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References:

[1] R.V. Chacon and J.B. Walsh, One-dimensional potential embedding , Lecture Notes Math. 511 , Springer, Berlin, 1976. · Zbl 0329.60041
[2] P.-A. Meyer, Probability and potentials , Blaisdell, Waltham, 1966. · Zbl 0138.10401
[3] A. Paszkiewicz, On distributions of conditional expectations , Probab. Math. Stat. 20 (2000), 287-291. · Zbl 0987.60021
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