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Viscosity solutions for second order integro-differential equations without monotonicity condition: the probabilistic approach

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In this paper, we establish a new existence and uniqueness result of a continuous viscosity solution for integro-partial differential equation (IPDE in short). The novelty is that we relax the so-called monotonicity assumption on the driver which is classically assumed in the literature of viscosity solutions of equation with non-local terms. Our method strongly relies on the link between IPDEs and backward stochastic differential equations with jumps for which we already know that the solution exists and is unique for general drivers. In the second part of the paper, we deal with the IPDE with obstacle and we obtain similar results.
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Keywords: 60H30; Integro-differential equation; backward stochastic differential equation with jumps; non-local term; viscosity solution

Document Type: Research Article

Affiliations: LMM, Université du Maine, Le Mans, France.

Publication date: May 18, 2016

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