This article is cited in 1 paper

Mathematics

On refinements of neo-classical inequality and its applications to stochastic differential equations and Brownian motion

D. S. Donchev^a, S. M. Sitnik^b, E. L. Shishkina<sup>c

a</sup> Sofia University "St. Kliment Okhridski", Sofia, Bulgaria
^b Belgorod State National Research University, Belgorod, Russia
^c Voronezh State University, Voronezh, Russia

Abstract: In this article some estimates are refined for the best constant in the well-known so called neo-classical inequality, which is the generalization of the Newton binomial formula in terms of Wright — Fox functions. The results of this article are applied to stochastic differential equations, Brownian motion and estimates of probability distributions.

Keywords: neo-classical inequality, stochastic differential inequality, Wright — Fox function, Berry — Essen inequality, Meller — König — Zeller operators.

Received: 09.10.2017
Revised: 20.10.2017

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