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Viscosity solutions of second order integral-partial differential equations: A new result

We show existence and uniqueness of a continuous with polynomial growth viscosity solution of a system of second order integral-partial differential equations (IPDEs for short) without assuming the usual monotonicity condition of the generator with respect to the jump component as in Barles et al.'s article \cite{BarlesBuckPardoux}. The Lévy measure is arbitrary and not necessarily finite. In our study the main tool we used is the notion of backward stochastic differential equations with jumps.