Orateur
Prof.
Said Hamadène
(Université du Maine)
Description
In this talk, we discuss 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 solution of equation with a non local term. Our method is based on the link of those IPDEs with backward stochastic differential equations (BSDEs in short) with jumps for which we already know that the solution exists and is unique.
References:
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Henri Poincaré. Analyse non linéaire, Elsevier 13(3), pp. 293-317, 1996.*
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83, 1997.*
- [3] Barles, G. and Imbert, C., Second-Order Elliptic Integro-Differential Equations : Viscosity Solutions' Theory
Revisited, *Ann. Inst. H. Poincaré- Anal. Non Linéaire 25(3): 567-585, 2008.*
- [4] Dumetrescu R., Quenez M.-C., Sulem A., Reflected BSDEs with jumps and partial integro-differential varia-
tional inequalities, *Research Report No 8213, Project-Teams Mathrisk (2013).*
- [5] Hamadène S., Ouknine Y., Reflected backward stochastic differential equation with jumps and random obstacle, *Electron. J. Probab., 8: 2 - 20, 2003.*
- [6] Harraj N., Ouknine Y. and Turpin I., Double barriers Reflected BSDEs with jumps and viscosity solutions of
parabolic Integro-differential PDEs, *Journal of Applied Mathematics and Stochastic Analysis, 1: 37-53, 2005.*
- [7] Tang, S.J. and Li, X.J., Necessary conditions for optimal control of stochastic systems with random jumps,
*SIAM J. Control Optim. 32: 14471475, 1994.*
Auteur principal
Prof.
Said Hamadène
(Université du Maine)
