Stochastic Theorem Research Articles

Viability of stochastic semi-linear control systems via the quasi-tangency condition

In this paper, we study a criterion for the viability of stochastic semi-linear control systems on a real, separable Hilbert space. The necessary and sufficient conditions are given using the notion of stochastic quasi-tangency. As a consequence, we prove that approximate viability and the viability property coincide for stochastic linear control systems. We obtain Nagumo's stochastic theorem and we present a method allowing to provide explicit criteria for the viability of smooth sets. We analyse the conditions characterizing the viability of the unit ball. The paper generalizes recent results from the deterministic framework.