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Start Over Subject Kurzweil integral

2. A nonexistence result for the Kurzweil integral

Creator:
Krejčí, Pavel and Kurzweil, Jaroslav
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Kurzweil integral and regulated functions
Language:
English
Description:
It is shown that there exist a continuous function f and a regulated function g defined on the interval [0,1] such that g vanishes everywhere except for a countable set, and the K *-integral of f with respect to g does not exist. The problem was motivated by extensions of evolution variational inequalities to the space of regulated functions.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

3. Adjoint classes of functions in the $H\sb 1$ sense

Creator:
Sworowski, Piotr
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Stieltjes integral, Kurzweil integral, Henstock integral, ${\mathrm H}_1$-integral, Riemann-Lebesgue theorem, variational measure, and adjoint classes
Language:
English
Description:
Using the concept of the $ {\mathrm H}_1$-integral, we consider a similarly defined Stieltjes integral. We prove a Riemann-Lebesgue type theorem for this integral and give examples of adjoint classes of functions.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

4. The Kurzweil integral in financial market modeling

Creator:
Krejčí, Pavel, Lamba, Harbir, Monteiro, Giselle Antunes, and Rachinskii, Dmitrii
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
hysteresis, Prandtl-Ishlinskii operator, Kurzweil integral, and market model
Language:
English
Description:
Certain financial market strategies are known to exhibit a hysteretic structure similar to the memory observed in plasticity, ferromagnetism, or magnetostriction. The main difference is that in financial markets, the spontaneous occurrence of discontinuities in the time evolution has to be taken into account. We show that one particular market model considered here admits a representation in terms of Prandtl-Ishlinskii hysteresis operators, which are extended in order to include possible discontinuities both in time and in memory. The main analytical tool is the Kurzweil integral formalism, and the main result proves the well-posedness of the process in the space of right-continuous regulated functions.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

5. The Kurzweil integral with exclusion of negligible sets

Creator:
Krejčí , Pavel
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Kurzweil integral and Young integral
Language:
English
Description:
We propose an extended version of the Kurzweil integral which contains both the Young and the Kurzweil integral as special cases. The construction is based on a reduction of the class of δ-fine partitions by excluding small sets.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public