Article

Aequationes mathematicae

, Volume 86, Issue 1, pp 91-98

Open Access This content is freely available online to anyone, anywhere at any time.

Remarks on strongly convex stochastic processes

  • Dawid KotrysAffiliated withDepartment of Mathematics and Computer Science, University of Bielsko–Biała Email author 

Abstract

Strongly convex stochastic processes are introduced. Some well-known results concerning convex functions, like the Hermite–Hadamard inequality, Jensen inequality, Kuhn theorem and Bernstein–Doetsch theorem are extended to strongly convex stochastic processes.

Mathematics Subject Classification (1991)

Primary 26A51 Secondary 26D15 39B62 60G99

Keywords

Strongly convex stochastic process Hermite–Hadamard inequality Jensen inequality Bernstein-Doetsch theorem Kuhn theorem mean-square integral