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Properties of generalized set-valued stochastic integrals

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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.

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1 Discussiones Mathematicae, Differential Inclusions, Control and Optimization

1 Kisielewicz M.

1 2014

Wyniki wyszukiwania

Properties of generalized set-valued stochastic integrals