Infinite horizon backward stochastic Volterra integral equations and discounted control problems

Infinite horizon backward stochastic Volterra integral equations (BSVIEs for short) are investigated. We prove the existence and uniqueness of adapted M-solution in a weighted $L^2$-space. Furthermore, we extend some important known results finite BSVIEs to infinite setting. provide variation constant formula class linear duality principle between (forward) equation (SVIE an BSVIE As application, investigate control problems SVIEs with discounted cost functional. establish both necessary sufficient conditions optimality by means Pontryagin's maximum principle, where adjoint is described as BSVIE. These applied fractional differential integro-differential equations.