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Properties of generalized set-valued stochastic integrals

100%

Kisielewicz M.

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

2014

tom 34

nr 1

131-147

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 by E.J. Jung and J.H. Kim, are not integrably bounded. Generalized set-valued stochastic integrals, considered in the paper, are in some non-trivial cases square integrably bounded and can be applied in the theory of stochastic differential equations with set-valued solutions.

Note on the selection properties of set-valued semimartingales

100%

Michta M.

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

1996

tom 16

nr 2

161-169

Set-valued semimartingales are introduced as an extension of the notion of single-valued semimartingales. For such multivalued processes their semimartingale selection properties are investigated.

Relaxation theorem for set-valued functions with decomposable values

88%

Kisielewicz A.

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

1996

tom 16

nr 1

91-97

Let (T,F,μ) be a separable probability measure space with a nonatomic measure μ. A subset K ⊂ L(T,Rⁿ) is said to be decomposable if for every A ∈ F and f ∈ K, g ∈ K one has $fχ_A + gχ_{T\A} ∈ K$. Using the property of decomposability as a substitute for convexity a relaxation theorem for fixed point sets of set-valued function is given.

Ograniczanie wyników

3 Discussiones Mathematicae, Differential Inclusions, Control and Optimization

1 Kisielewicz A.

1 Kisielewicz M.

1 Michta M.

1 2014

2 1996

Wyniki wyszukiwania

Properties of generalized set-valued stochastic integrals

Note on the selection properties of set-valued semimartingales

Relaxation theorem for set-valued functions with decomposable values