Displaying similar documents to “Note on the selection properties of set-valued semimartingales”

Boundedness of set-valued stochastic integrals

Michał Kisielewicz (2015)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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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...

Properties of set-valued stochastic integrals

Jerzy Motyl, Joachim Syga (2006)

Discussiones Mathematicae Probability and Statistics

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We introduce set-valued stochastic integrals driven by a square-integrable martingale and by a semimartingale. We investigate properties of both integrals.

Properties of generalized set-valued stochastic integrals

Michał Kisielewicz (2014)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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The paper is devoted to properties of generalized set-valued stochastic integrals defined in [10]. These integrals generalize set-valued stochastic integrals defined by E.J. Jung and J.H. Kim in the paper [4]. Up to now we were not able to construct any example of set-valued stochastic processes, different on a singleton, having integrably bounded set-valued integrals defined in [4]. It was shown by M. Michta (see [11]) that in the general case set-valued stochastic integrals defined...

Set-valued Stratonovich integral

Anna Góralczyk, Jerzy Motyl (2006)

Discussiones Mathematicae Probability and Statistics

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The purpose of the paper is to introduce a set-valued Stratonovich integral driven by a one-dimensional Brownian motion. We discuss the existence of this integral and investigate its properties.