Abstract
Recently, in the class of convex stochastic processes, Kotrys (Aequat Math 83:143–151, 2012; Aequat Math 86:91–98, 2013) proposed upper and lower bounds of mean-square stochastic integrals by using Hermite–Hadamard inequality. This paper shows that these bounds can be refined. Our results extend and refine the corresponding ones in the literature. Finally, an open problem for further investigations is given.
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References
Kotrys D.: Hermite–Hadamard inequality for convex stochastic processes. Aequat. Math. 83, 143–151 (2012)
Kotrys D.: Remarks on strongly convex stochastic processes. Aequat. Math. 86, 91–98 (2013)
Nikodem K.: On convex stochastic processes. Aequat. Math. 20, 184–197 (1980)
Shaked M., Shanthikumar J.G.: Stochastic convexity and its applications. Adv. Appl. Prob. 20, 427–446 (1988)
Skowroński A.: On some properties of J-convex stochastic processes. Aequat. Math. 44, 249–258 (1992)
Sobczyk K.: Stochastic Differential Equations with Applications to Physics and Engineering. Kluwer, Dordrecht (1991)
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Agahi, H. Refinements of mean-square stochastic integral inequalities on convex stochastic processes. Aequat. Math. 90, 765–772 (2016). https://doi.org/10.1007/s00010-015-0378-7
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DOI: https://doi.org/10.1007/s00010-015-0378-7