Strong and weak solutions to stochastic inclusions

• Autorzy: Michał Kisielewicz
• Języki publikacji: EN

Abstrakty

EN

Existence of strong and weak solutions to stochastic inclusions $x_{t} - x_{s} ∈ ∫^{t}_{s} F_{τ}(x_{τ})dτ + ∫^{t}_{s} G_{τ}(x_{τ})dw_{τ} + ∫^{t}_{s} ∫_{ℝ^{n}} H_{τ,z}(x_{τ})q(dτ,dz)$ and $x_{t} - x_{s} ∈ ∫^{t}_{s} F_{τ}(x_{τ})dτ + ∫^{t}_{s}G_{τ}(x_{τ})dw_{τ} + ∫^{t}_{s}∫_{|z|≤1} H_{τ,z}(x_{τ})q(dτ,dz) + ∫^{t}_{s}∫_{|z|>1} H_{τ,z}(x_{τ})p(dτ,dz)$, where p and q are certain random measures, is considered.

Słowa kluczowe

EN

strong and weak solutions; stochastic inclusions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1995
• Tom: 32
• Numer: 1
• Strony: 277-286

Daty

wydano

1995

Twórcy

autor

Michał Kisielewicz

• Institute of Mathematics, Higher College of Engineering, Podgórna 50, 65-246 Zielona Góra, Poland

Bibliografia

• [1] A. V. Skorohod, Studies in the Theory of Random Processes, Dover, New York, 1982.
• [2] M. Kisielewicz, Differential Inclusions and Optimal Control, Kluwer Acad. Publ. and Polish Sci. Publ., Warszawa-Dordrecht, 1991.
• [3] M. Kisielewicz, Properties of solution set of stochastic inclusions, J. Appl. Math. Stochastic Anal. 6 (1993), 217-236.
• [4] M. Kisielewicz, Existence of strong solutions to stochastic inclusions, Discuss. Math. 15 (submitted).
• [5] P. Protter, Stochastic Integration and Differential Equations, Springer, Berlin, 1990.