On some properties of \(J\)-convex stochastic processes
type: Item
instance of: scholarly article
title: On some properties of \(J\)-convex stochastic processes
zbMATH Open document ID: 0764.60040
DOI: 10.1007/BF01830983
author: Arkadiusz Skowroński
published in: Aequationes Mathematicae
publication date: 1993-04-01T00:00:00Z
full work available at URL: https://eudml.org/doc/137496
review text: Some results on the differentiability of convex stochastic processes are presented. Next the following stochastic version of a theorem by Ng, Nikodem, Kominek on \(J\)-convex functions majorized by \(J\)-concave functions is given: Let \((\Omega,{\mathcal A},P)\) be a probability space and \((a,b)\subset\mathbb{R}\) be an open interval. If stochastic processes \(X_ 1,X_ 2: (a,b)\times\Omega\to\mathbb{R}\) are \(J\)-convex and \(J\)-concave, respectively, and for every \(t\in(a,b)\) satisfy the inequality \(X_ 1(t,\cdot)\leq X_ 2(t,\cdot)\) (a.e.), then there exist stochastic processes \(Y_ 1,Y_ 2:(a,b)\times\Omega\to\mathbb{R}\) and \(A:(a,b)\times\Omega\to\mathbb{R}\) such that \(Y_ 1\) is convex, \(Y_ 2\) is concave, \(A\) is additive and \(X_ 1=A+Y_ 1\) and \(X_ 2=A+Y_ 2\).
reviewed by: Andrzej Skowroński
Mathematics Subject Classification ID: 60G07
Mathematics Subject Classification ID: 26A51
Mathematics Subject Classification ID: 39B72
Mathematics Subject Classification ID: 26A15
Mathematics Subject Classification ID: 26A24
Mathematics Subject Classification ID: 60G99
Mathematics Subject Classification ID: 60H99
Mathematics Subject Classification ID: 60K99
zbMATH DE Number: 149475
zbMATH Keywords: differentiability of convex stochastic processes
MaRDI profile type: Publication
cites work: Q4197800
cites work: On a problem of K. Nikodem
cites work: On a generalization of the Cauchy equation
cites work: On Midconvex Functions with Midconcave Bounds
cites work: Midpoint convex functions majorized by midpoint concave functions
cites work: On convex stochastic processes
OpenAlex ID: W2329743731
description: scientific article; zbMATH DE number 149475