A1 - Góralczyk, Anna
N2 - The subject of research included in doctoral dissertation are properties of strong solutions' sets of two kinds of Stratonovich type stochastic inclusions. In the first inclusion the set valued Stratonovich type integral driven by Wiener process is defined for Hukuhara differentiable set valued function. Properties of set valued Stratonovich type integral researched in dissertation were used to examine properties of strong solutions' set of Stratonovich type inclusion.
N2 - There was proved existence of strong solution of the first inclusion and closedness of strong solutions' set of this inclusion. Whereas in the second inclusion set valued Stratonovich type integral with respect to continuous semimartingale is defined for upper separated set valued function. In this inclusion apart from set valued Stratonovich type integral there is set valued integral of upper separated set valued function with respect to continuous adapted process and set valued integral of maximal monotone set valued function driven by quadratic variation process of continuous semimartingale.
N2 - The main result related to the second inclusion is theorem, which gives conditions for existence of strong solution of this inclusion. This theorem extends results of M. Michta and J. Motyl from paper "Set valued Stratonovich integral and Stratonovich type stochastic inclusion" to instance with maximal monotone set valued function. Similar problem but for Itô inclusion was studied by R. Pettersson in "Yosida approximations for multivalued stochastic differential equations".
KW - pochodna Hukuhary
KW - Multifunkcja
KW - istnienie i własności zbioru rozwiązań stochastycznych inkluzji typu Stratonowicza
KW - wielowartościowe całki typu Stratonowicza
KW - stochastyczne inkluzje typu Stratonowicza
T1 - Własności zbioru rozwiązań inkluzji stochastycznych typu Stratonowicza