THE NARROWING SET-VALUED STOCHASTIC INTEGRAL EQUATIONS

We analyze set-valued stochastic integral equations whose solutions are mappings with values in the hyperspace of subsets of square integrable random vectors space. In this paper we give a new formulation of these equations resulting in a new property of solutions. Namely, the diameter of the solution values will be a nonincreasing function. Hence we call these equations “narrowing”. We prove a result on existence and uniqueness of the solution to the narrowing setvalued stochastic integral equations. We establish a boundedness type result for the solution and an error of an approximate solution. Also the continuous dependence of the solution with respect to data of the equation is shown.