### Properties of solution set of stochastic inclusions.

Kisielewicz, Michał (1993)

Journal of Applied Mathematics and Stochastic Analysis

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Kisielewicz, Michał (1993)

Journal of Applied Mathematics and Stochastic Analysis

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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.

T. Barth, A. U. Kussmaul (1981)

Annales scientifiques de l'Université de Clermont. Mathématiques

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Michel Métivier (1982)

Séminaire de probabilités de Strasbourg

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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.

Svetlana Janković (1998)

Zbornik Radova

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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.

Michał Kisielewicz (2006)

Discussiones Mathematicae Probability and Statistics

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Some sufficient conditins for tightness of continuous stochastic processes is given. It is verified that in the classical tightness sufficient conditions for continuous stochastic processes it is possible to take a continuous nondecreasing stochastic process instead of a deterministic function one.

Z. Ivković, J. Vukmirović (1976)

Matematički Vesnik

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J. M. Angulo Ibáñez, R. Gutiérrez Jáimez (1988)

Annales scientifiques de l'Université de Clermont-Ferrand 2. Série Probabilités et applications

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Anna Chojnowska-Michalik (1979)

Banach Center Publications

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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.

Marek T. Malinowski, Ravi P. Agarwal (2017)

Czechoslovak Mathematical Journal

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We analyse multivalued stochastic differential equations driven by semimartingales. Such equations are understood as the corresponding multivalued stochastic integral equations. Under suitable conditions, it is shown that the considered multivalued stochastic differential equation admits at least one solution. Then we prove that the set of all solutions is closed and bounded.