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Boundedness of set-valued stochastic integrals

100%

Kisielewicz M.

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

2015

tom 35

nr 2

197-207

The paper deals with integrably boundedness of Itô set-valued stochastic integrals defined by E.J. Jung and J.H. Kim in the paper [4], where has not been proved that this integral is integrably bounded. The problem of integrably boundedness of the above set-valued stochastic integrals has been considered in the paper [7] and the monograph [8], but the problem has not been solved there. The first positive results dealing with this problem due to M. Michta, who showed (see [11]) that there are bounded set-valued 𝔽-nonanticipative mappings having unbounded Itô set-valued stochastic integrals defined by E.J. Jung and J.H. Kim. The present paper contains some new conditions implying unboundedness of the above type set-valued stochastic integrals.

Trivial bundles of spaces of probability measures and countable-dimensionality

88%

Gutev V. G.

Studia Mathematica

1995

tom 114

nr 1

1-11

The probability measure functor P carries open continuous mappings $f: X onto → Y$ of compact metric spaces into Q-bundles provided Y is countable-dimensional and all fibers $f^{-1}(y)$ are infinite. This answers a question raised by V. Fedorchuk.

Fractals of generalized F− Hutchinson operator

88%

Nazir T., Silvestrov S., Abbas M.

Waves, Wavelets and Fractals

2016

tom 2

nr 1

The aim of this paper is to construct a fractal with the help of a finite family of F− contraction mappings, a class of mappings more general than contraction mappings, defined on a complete metric space. Consequently, we obtain a variety of results for iterated function systems satisfying a different set of contractive conditions. Some examples are presented to support the results proved herein. Our results unify, generalize and extend various results in the existing literature.

Ograniczanie wyników

1 Discussiones Mathematicae, Differential Inclusions, Control and Optimization

1 Studia Mathematica

1 Waves, Wavelets and Fractals

1 Abbas M.

1 Gutev V. G.

1 Kisielewicz M.

1 Nazir T.

1 Silvestrov S.

1 2016

1 2015

1 1995

Wyniki wyszukiwania

Boundedness of set-valued stochastic integrals

Trivial bundles of spaces of probability measures and countable-dimensionality

Fractals of generalized F− Hutchinson operator