Completion measurable linear functionals on a probability space
Marek Kanter (1978)
Colloquium Mathematicae
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Marek Kanter (1978)
Colloquium Mathematicae
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Michał Kisielewicz (2001)
Discussiones Mathematicae Probability and Statistics
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Some special selections theorems for stochastic set-valued integrals with respect to the Lebesgue measure are given.
Joachim Syga (2015)
Discussiones Mathematicae Probability and Statistics
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A random measure associated to a semimartingale is introduced. We use it to investigate properties of several types of stochastic integrals and properties of the solution set of Stratonovich-type stochastic inclusion.
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...
Z. Ivković, Yu. A. Rozanov (1972)
Publications de l'Institut Mathématique
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M. Métivier, J. Pellaumail (1977)
Publications mathématiques et informatique de Rennes
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Michał Kisielewicz (1999)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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The definition and some existence theorems for stochastic differential inclusion dZₜ ∈ F(Zₜ)dXₜ, where F and X are set valued stochastic processes, are given.
Michał Kisielewicz (1997)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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The definition and some existence theorems for stochastic differential inclusions depending only on selections theorems are given.
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...
Artstein, Zvi, Wets, Roger J.B. (1995)
Journal of Convex Analysis
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M. Métivier, J. Pellaumail (1976)
Publications mathématiques et informatique de Rennes
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Fabio Bagarello (2006)
Banach Center Publications
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Sridharan, V., Kalyani, T.V. (2005)
APPS. Applied Sciences
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J. Gani (1966-1967)
Publications mathématiques et informatique de Rennes
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Michael Weba (1986)
Mathematische Zeitschrift
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Władysław Sosulski (2001)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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We present the concepts of set-valued stochastic integrals in a plane and prove the existence of a solution to stochastic integral inclusions of the form
Nicolas Privault (1998)
Banach Center Publications
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The aim of this paper is the study of a non-commutative decomposition of the conservation process in quantum stochastic calculus. The probabilistic interpretation of this decomposition uses time changes, in contrast to the spatial shifts used in the interpretation of the creation and annihilation operators on Fock space.
Micha Kisielewicz (2003)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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The Girsanov's theorem is useful as well in the general theory of stochastic analysis as well in its applications. We show here that it can be also applied to the theory of stochastic differential inclusions. In particular, we obtain some special properties of sets of weak solutions to some type of these inclusions.