Jerzy Motyl

Stochastic functional inclusion driven by semimartingale

We define a set-valued stochastic process and an integral of a such process with respect to a semimartingale. Next we consider a stochastic integral inclusion. Using fixed point methods we prove some results on the existence of its solutions

Viable solutions of set-valued stochastic equation

The existence of viable solutions to set-valued Itô equation, i.e., solutions remaining at any time in a ilxed sublet of a slate space, is established for a functional inclusion with dissipative set-valued operators which need not he Lipsehitz continuous nor have to satisfy the Pardoux “monotone” property

Second Order Stochastic Inclusion

Abstract The purpose of the paper is to consider some stochastic control problems as a particular case of a more general theory, the stochastic inclusions theory. We discuss the existence of weak solutions to a stochastic inclusion of second order, driven by two general semimartingales. Finally we present some examples.

Convex selections of multifunctions and their applications

The notion of upper separated set-valued functions which forms a necessary and sufficient condition for the existence of convex selections for convex-valued multifunctions is introduced. The results obtained in this article lead to a new class of the multifunctions admitting continuous selections and therefore they are applicable to the existence of solutions to differential and stochastic inclusions. †Dedicated to N.U. Ahmed on the occassion of his 70th birthday.

High Order Stochastic Inclusions and Their Applications

Abstract The purpose of the paper is to consider some stochastic control problems as a particular case of a more general theory, the stochastic inclusions theory. We discuss the existence of weak solutions to stochastic inclusion of a second order. The considered investigations follow with some technical and financial problems.

On the minimal solution property of neutral functional-differential inclusion

Abstract The neutral functional-differential inclusion a x (t) ϵ F(t, x t , a x t ) is consid assume the inclusion possesses a solution. Then a sufficient condition for this solution to admit a minimal L1-norm (to be a “slow solution”) is given. Some properties of this condition, called “integral dissipativity,” are obtained.