Scorza Dragoni type theorems
Sections in function spaces
Selected results on measurable selections
Selection from Upper Semi-Continuous Compact-Valued Mappings.
Selections of set-valued stochastic processes.
Selections using orderings (non-separable case)
Separation properties in and measurable multifunctions and graphs
Set valued measures and integral representation
The extension theorem of bounded, weakly compact, convex set valued and weakly countably additive measures is established through a discussion of convexity, compactness and existence of selection of the set valued measures; meanwhile, a characterization is obtained for continuous, weakly compact and convex set valued measures which can be represented by Pettis-Aumann-type integral.
Set-valued and fuzzy stochastic integral equations driven by semimartingales under Osgood condition
We analyze the set-valued stochastic integral equations driven by continuous semimartingales and prove the existence and uniqueness of solutions to such equations in the framework of the hyperspace of nonempty, bounded, convex and closed subsets of the Hilbert space L2 (consisting of square integrable random vectors). The coefficients of the equations are assumed to satisfy the Osgood type condition that is a generalization of the Lipschitz condition. Continuous dependence of solutions with respect...
Set-valued integration in seminorm. II.
Set-valued random differential equations in Banach space
We consider the problem of the existence of solutions of the random set-valued equation: (I) , t ∈ [0,T] -a.e.; X₀ = U p.1 where F and U are given random set-valued mappings with values in the space , of all nonempty, compact and convex subsets of the separable Banach space E. Under certain restrictions on F we obtain existence of solutions of the problem (I). The connections between solutions of (I) and solutions of random differential inclusions are investigated.
Sobre los teoremas de Lyapunov y de Radon-Nikodym.
Some applications of Girsanov's theorem to the theory of stochastic differential inclusions
The Girsanov's theorem is useful as well in the general theory of stochastic analysis as well in its applications. We show here that it can be also applied to the theory of stochastic differential inclusions. In particular, we obtain some special properties of sets of weak solutions to some type of these inclusions.
Some remarks on the relation of classical set-valued mappings to the Baire classification
Some theorems of Scorza-Dragoni type for multifunctions with application to the problem of existence of solutions for differential multivalued equations
Some theorems on measurable and continuous selections and some applications
Sur les sélecteurs des multifonctions
Sur l'espérance conditionnelle multivoque non convexe