Viability theorems for stochastic inclusions

• Autorzy: Michał Kisielewicz
• Języki publikacji: EN

Abstrakty

EN

Sufficient conditions for the existence of solutions to stochastic inclusions $x_t - x_s ∈ ∫^t_s F_τ(x_τ)dτ + ∫^t_s G_τ(x_τ)dw_τ + ∫^t_s∫_{IRⁿ} H_{τ,z}(x_τ)ν̃ (dτ,dz)$ beloning to a given set K of n-dimensional cádlág processes are given.

Słowa kluczowe

EN

stochastic processes; stochastic inclusions; optimal control

Kategorie tematyczne

• 93B05: Controllability
• 93C30: Systems governed by functional relations other than differential equations (such as hybrid and switching systems)

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
• Rocznik: 1995
• Tom: 15
• Numer: 1
• Strony: 61-42

Daty

wydano

1995

Twórcy

autor

Michał Kisielewicz

• Institute of Mathematics, Technical University, Podgórna 50, 65-246 Zielona Góra, Poland

Bibliografia

• [1] J. P. Aubin, and A. Cellina, Differential Inclusions, Springer-Verlag 1984.
• [2] J. P. Aubin and H. Frankowska, Set-Valued Analysis, Birkhäser 1990.
• [3] F. Hiai, and H. Umegaki, Integrals, conditional expections and martingals of multifunctions, J. Multivariate Anal. 7 (1977), 149-182.
• [4] M. Kisielewicz, Set-valued stochastic integrals and stochastic inclusions, Journal of Stochastic Analysis and Applications (submitted to print).
• [5] M. Kisielewicz, Properties of solution set of stochastic inclusions, Journal of Appl. Math. and Stochastic Analysis 6 (3) (1993), 217-236.
• [6] M. Kisielewicz, Differential Inclusions and Optimal Control, Kluwer Acad. Publ. and Polish Sci. Publ. Warszawa - Dordrecht - Boston - London (1991).
• [7] N. S. Papageorgiou, Decomposable sets in the Lebesgue-Bochner spaces, Comm. Math. Univ. Sancti Pauli 37 (1) (1988), 49-62.
• [8] Ph. Protter, Stochastic Integration and Differential Equations, Springer-Verlag (1990), Berlin - Heildelberg - New York.