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This paper is concerned with a discounted optimal control problem ofpartially observed forward-backward stochastic systems with jumps on infinitehorizon. The control domain is convex and a kind of infinite horizonobservation equation is introduced. The uniquely solvability of infinitehorizon forward (backward) stochastic differential equation with jumps isobtained and more extended analysis, especially for the backward case, is made.Some new estimates are first given and proved for the critical variationalinequality. Then an ergodic maximum principle is obtained by introducing someinfinite horizon adjoint equations whose uniquely solvabilities are guaranteednecessarily. Finally, some comparison are made with two kinds of representativeinfinite horizon stochastic systems and their related optimal controls.

The Maximum Principle for Discounted Optimal Control of Partially Observed Forward-Backward Stochastic Systems with Jumps on Infinite Horizon