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Start Over Subject integration-by-parts

1. On Itô-Kurzweil-Henstock integral and integration-by-part formula

Creator:
Toh, Tin-Lan and Chew, Tuan-Seng
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
generalized Riemann approach, stochastic integral, and integration-by-parts
Language:
English
Description:
In this paper we derive the Integration-by-Parts Formula using the generalized Riemann approach to stochastic integrals, which is called the Itô-Kurzweil-Henstock integral.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. On Kurzweil-Stieltjes integral in a Banach space

Creator:
Monteiro, Giselle A. and Tvrdý, Milan
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Kurzweil-Stieltjes integral, substitution formula, and integration-by-parts
Language:
English
Description:
In the paper we deal with the Kurzweil-Stieltjes integration of functions having values in a Banach space X. We extend results obtained by Štefan Schwabik and complete the theory so that it will be well applicable to prove results on the continuous dependence of solutions to generalized linear differential equations in a Banach space. By Schwabik, the integral ∫ b a d[F]g exists if F : [a, b] → L(X) has a bounded semi-variation on [a, b] and g : [a, b] → X is regulated on [a, b]. We prove that this integral has sense also if F is regulated on [a, b] and g has a bounded semi-variation on [a, b]. Furthermore, the integration by parts theorem is presented under the assumptions not covered by Schwabik (2001) and Naralenkov (2004), and the substitution formula is proved.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public