  This paper deals with the stochastic control of nonlinear systems in the
presence of state and control constraints, for uncertain discrete-time dynamics
in finite dimensional spaces. In the deterministic case, the viability kernel
is known to play a basic role for the analysis of such problems and the design
of viable control feedbacks. In the present paper, we show how a stochastic
viability kernel and viable feedbacks relying on probability (or chance)
constraints can be defined and computed by a dynamic programming equation. An
example illustrates most of the assertions.
