Displaying similar documents to “Properties of solution set of stochastic inclusions.”

Stochastic differential inclusions

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.

On solutions set of a multivalued stochastic differential equation

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.

Stochastic differential inclusions

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.

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...