  In this article, the sufficient Pontryagin's maximum principle for infinite
horizon discounted stochastic control problem is established. The sufficiency
is ensured by an additional assumption of concavity of the Hamiltonian
function. Throughout the paper, it is assumed that the control domain U is a
convex set and the control may enter the diffusion term of the state equation.
The general results are applied to the controlled stochastic logistic equation
of population dynamics.
