Michał Kisielewicz

Set-valued stochastic intergrals and stochastic inclutions 1

We present the concepts of set - valued stochastic integrals and stochastic inclusions. The main result of the paper deals with a selection property of set - valued stochastic integrals. This property is a fundamental one for stochastic inclusions.

Multivalued differential equations in separable Banach spaces

AbstractThis paper is concerned with multivalued differential equations of the form

Properties of solution set of stochastic inclusions

\dot x

Stochastic Differential Inclusions

∈F(t,x), whereF is a multivalued mapping taking as its values nonempty compact, but not necessarily convex, subsets in a separable Banach space. The main result is connected with the existence of solutions of these equations.

Weak Compactness of Solution Sets to Stochastic Differential Inclusions with Non-Convex Right-Hand Sides

Preface.- List of Symbols.- 1. Stochastic Processes.- 2. Set-Valued Stochastic Processes.- 3. Set-Valued Stochastic Intergrals.- 4. Stochastic Differential Inclusions.- 5.Viability Theory.- 6. Partial Differential Inclusions.- 7. Some Optimal Control Problems.- Bibliography.- Subject Index.

EXISTENCE THEOREM FOR FUNCTIONAL-DIFFERENTIAL EQUATION WITH COMPACT CONVEX VALUED SOLUTIONS

The properties of the solution set of stochastic inclusions xt−xs∈clL2(∫stFτ(xτ)dτ

Existence theorem for nonconvex stochastic inclusions

Necessary and sufficient conditions for the existence of weak solutions to stochastic differential inclusions with convex right-hand sides are given. The main results of the paper deal with the weak compactness with respect to the convergence in distribution of solution sets to such inclusions.

Set-Valued Stochastic Processes

This chapter is devoted to the theory of stochastic differential inclusions. The main results deal with stochastic functional inclusions defined by set-valued functional stochastic integrals. Subsequent sections discuss properties of stochastic and backward stochastic differential inclusions.