Sufficient Stochastic Maximum Principle for Discounted Control Problem
  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. 
Bohdan Maslowski, Petr Veverka
math.OC cs.SY math.PR