Set-valued stochastic integrals and stochastic inclusions in a plane

• Autorzy: Władysław Sosulski
• Języki publikacji: EN

Abstrakty

EN

We present the concepts of set-valued stochastic integrals in a plane and prove the existence of a solution to stochastic integral inclusions of the form
$z_{s,t} ∈ φ_{s,t} + ∫_{0}^{s} ∫_{0}^{t} F_{u,v}(z_{u,v})dudv + ∫_{0}^{s} ∫_{0}^{t}G_{u,v}(z_{u,v})dw_{u,v}$

Słowa kluczowe

EN

stochastic inclusions in the plane; set-valued random field; two-parameter stochastic process; weak compactness

Kategorie tematyczne

• 93E03: Stochastic systems, general
• 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: 2001
• Tom: 21
• Numer: 2
• Strony: 249-259

Daty

wydano

2001

otrzymano

2001-10-10

poprawiono

2001-11-18

Twórcy

autor

Władysław Sosulski

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

Bibliografia

• [1] R. Cairoli, Sur une équation differentielle stochastique, Compte Rendus Acad. Sc. Paris 274 (A) (1972), 1739-1742.
• [2] R. Cairoli and J.B. Walsh, Stochastic integrals in the plane, Acta Mathematica 134 (1975), 112-183.
• [3] F. Hiai and H. Umegaki, Integrals, conditional expectations, and martingales of multivalued functions, J. Multivar. Anal. 7 (1977), 149-162.
• [4] M. Kisielewicz, Differential Inclusions and Optimal Control, Kluwer Acad. Publ. - PWN, Dordrecht, Boston - London, Warszawa 1991.
• [5] M. Kisielewicz, Properties of solution set of stochastic inclusions, J. Appl. Math. Stoch. Anal. 6 (3) (1993), 217-236.
• [6] L. Ponomarenco, Stochastic integral with respect to the multiparameter Brownian motion and attached stochastic equations (in Russian), Teor. Veroiatn. i Mat. Stat. Kiev 7 (1972) 100-109.
• [7] W. Sosulski, Subtrajectory integrals of set-valued functions depending on parameters, Discuss. Math. 10 (1990), 99-121.
• [8] T.J. Tsarenco, On some scheme of the construction of stochastic integral for the radom field (in Russian), Kibernetika 1 (1972), 113-118.
• [9] C. Tudor, Stochastic integral equations in the plane, Preprint Series in Mathematics, INCREST 29 (1979) 507-538.

Identyfikatory

DOI

10.7151/dmgt.1027