@misc{Syga_Joachim_Wielowartościowe, author={Syga, Joachim}, howpublished={online}, language={pol}, abstract={Properties of set-valued stochastic integrals with respect to a semimartingale are the subject of the study contained in this dissertation. Some of these properties are used to the theory of stochastic inclusions. There are considered an Itô-type and a Stratonovich-type stochastic integrals. The dissertation is devided into four chapters.}, abstract={The first chapter contains basic definitions and properties. The second chapter contains a set-valued Itô-type stochastic integral. There are presented properties of a set of Itô-integrable selections of set-valued integrands and their connection with the properties of a set-valued Itô-type stochastic integral. Theorems on estimation the distance of set-valued stochastic integrals by the distance of set-valued integrands are the main results of this chapter.}, abstract={The construction of a set-valued Stratonovich-type stochastic integral is presented in the third chapter. It bases on the construction of a forward and a backward stochastic integrals introduced by F. Russo, P. Vallois and M. Errami. A selection theorem for a set-valued reversible stochastic process and an approximation theorem for a set-valued Stratonovich-type stochastic integral are the main results of this chapter.}, abstract={The fourth chapter contains a theorem on existence of strong solutions to an Itô-type stochastic inclusion and a theorem on boundedness of a set of strong solutions for such stochastic inclusion. A selection theorem for a set-valued Stratonovich-type stochastic integral is the last result of this chapter.}, title={Wielowartościowe całki stochastyczne względem semimartyngału i ich zastosowania w teorii inkluzji stochastycznych}, keywords={inkluzja stochastyczna typu Itô / typu Stratonowicza, wielowartościowa całka stochastyczna typu Itô / typu Stratonowicza, proces całkowo dekomponowalny (rozkładalny), proces odwracalny, proces z czasem odwróconym, wielowartościowy proces stochastyczny, semimartyngał odwracalny}, }