On invariance of linear subspaces for stochastic evolution equations

• Autorzy: Milian A.
• Języki publikacji: EN

Abstrakty

EN

In the paper we consider Ito equation on a Hilbert space. We give necessary and sufficient conditions ensuring the invariance property of linear subspaces of the state space by mild solutions to the equation.

Słowa kluczowe

EN

stochastic differential equations; invariance; subspace

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2001
• Tom: Vol. 34, nr 2
• Strony: 425--430
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Milian A.

• Institute of Mathematics Cracow University of Technology ul. Warszawska 24 31-155 Kraków, Poland

Bibliografia

• [1] Da Prato G., Zabczyk J., Stochastic Equations in Infinite Dimensions, 1992, Cambridge University Press.
• [2] Filipović D., Invariant Manifolds for Weak Solutions to Stochastic Equations, Working paper, Department of Mathematics, ETH, Switzerland (1999).
• [3] Goncharuk N., Kotelenez P., Fractional Step Method for Stochastic Evolution Equations, Preprint 96-144 (1996), 1-37.
• [4] Jachimiak W., Stochastic Invariance in Infinite Dimension, Preprint 591, Polish Acad. Sc. (Warsaw, 1998).
• [5] Kotelenez P., Comparison methods for a class of function valued stochastic partial differential equations, Probability Theory and Related Fields (1992), 1-19.
• [6] Milian A., Comparison Theorems for Stochastic Evolution Equations, Preprint 591, Polish Acad. Sc. (Warsaw, 1998).
• [7] Tessitore G., Zabczyk J., Comments on Transition Semigroups and Stochastic Invariance, Scuola Normale Superiore, Pisa, Preprint di Matematica, n.15 (1998), 1-15.