Quasi-retractive representation of solution sets to stochastic inclusions

On The Solution Sets Of Semicontinuous Quantum Stochastic Differential Inclusions∗

The aim of this paper is to provide a unified treatment of the existence of solution of both upper and lower semicontinuous quantum stochastic differential inclusions. The quantum stochastic differential inclusion is driven by operatorvalued stochastic processes lying in certain metrizable locally convex space. The unification of solution sets to these two discontinuous non-commutative stochast...

Continuous Interpolation of Solution Sets of Lipschitzian Quantum Stochastic Differential Inclusions

Given any finite set of trajectories of a Lipschitzian quantum stochastic differential inclusion (QSDI), there exists a continuous selection from the complex-valued multifunction associated with the solution set of the inclusion, interpolating the matrix elements of the given trajectories. Furthermore, the difference of any two of such solutions is bounded in the seminorm of the locally convex ...

Improving the Solution of Fuzzy Differential Inclusions

From Well-Quasi-Ordered Sets to Better-Quasi-Ordered Sets

We consider conditions which force a well-quasi-ordered poset (wqo) to be betterquasi-ordered (bqo). In particular we obtain that if a poset P is wqo and the set Sω(P ) of strictly increasing sequences of elements of P is bqo under domination, then P is bqo. As a consequence, we get the same conclusion if Sω(P ) is replaced by J (P ), the collection of non-principal ideals of P , or by AM(P ), ...

Stochastic differential inclusions of semimonotone type in Hilbert spaces

In this paper, we study the existence of generalized solutions for the infinite dimensional nonlinear stochastic differential inclusions $dx(t) in F(t,x(t))dt +G(t,x(t))dW_t$ in which the multifunction $F$ is semimonotone and hemicontinuous and the operator-valued multifunction $G$ satisfies a Lipschitz condition. We define the It^{o} stochastic integral of operator set-valued stochastic pr...