Displaying similar documents to “Existence of viable solutions for a nonconvex stochastic differential inclusion”

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.

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.

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.

Some applications of Girsanov's theorem to the theory of stochastic differential inclusions

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.

On differential equations and inclusions with mean derivatives on a compact manifold

S.V. Azarina, Yu.E. Gliklikh (2007)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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We introduce and investigate a new sort of stochastic differential inclusions on manifolds, given in terms of mean derivatives of a stochastic process, introduced by Nelson for the needs of the so called stochastic mechanics. This class of stochastic inclusions is ideologically the closest one to ordinary differential inclusions. For inclusions with forward mean derivatives on manifolds we prove some results on the existence of solutions.

Set-valued stochastic integrals and stochastic inclusions in a plane

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 z s , t ∈ φ s , t + ∫ 0 s ∫ 0 t F u , v ( z u , v ) d u d v + ∫ 0 s ∫ 0 t G u , v ( z u , v ) d w u , v

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...