  In this short note we formulate a infinite-horizon stochastic optimal control
problem for jump-diffusions of Ito-Levy type as a LP problem in a measure
space, and prove that the optimal value functions of both problems coincide.
The main tools are the dual formulation of the LP primal problem, which is
strongly connected to the notion of sub-solution of the partial
integro-differential equation of Hamilton-Jacobi-Bellman type associated with
the optimal control problem, and the Krylov regularization method for viscosity
solutions.
