Maximum principles for jump diffusion processes with infinite horizon

where X(t) is a controlled jump diffusion and u(t) is the control process. We allow for the case where the controller only has access to partial-information. Thus, we have a infinite horizon problem with partial information. Infinitehorizon optimal control problems arise in many fields of economics, in particular in models of economic growth. Note that because of the general nature of the partial information filtration Et, we cannot use dynamic programming and Hamilton-Jacobi-Bellman (HJB) equations to solve the optimization problem. Thus our problem is different from partial observation control problems.