# On Solutions to Set-Valued Stochastic Integral Equations and Inclusions

Mariusz Michta*

In the talk we give some connections between the theory of stochastic integral inclusions and the theory of set-valued stochastic integral equations. First we present results on existence, uniqueness and stability of solutions to set-valued integral equations. Next, we show that for every solution $X$ to the set-valued integral equation corresponding to the given stochastic integral inclusion, there exists a solution of the inclusion that is an $L^2$-continuous selection of $X$. It enables us to infer about the reachable sets and viability problems of solutions to stochastic integral inclusions.

Mathematics Subject Classification: 60H05 60G20

Keywords: stochastic integral inclusion, set-valued stochastic integaral equation

Minisymposion: Analysis and Control of Evolution Equations and Inclusions