caa a22 4500 606193936 CHVBK 20210128100911.0 cr unu---uuuuu 210128e20151201xx s 000 0 eng 10.1007/s00030-015-0338-x doi (NATIONALLICENCE)springer-10.1007/s00030-015-0338-x Systems of integro-PDEs with interconnected obstacles and multi-modes switching problem driven by Lévy process [Elektronische Daten] [Said Hamadène, Xuxhe Zhao] In this paper we show existence and uniqueness of the solution in viscosity sense for a system of nonlinear m variational integral-partial differential equations with interconnected obstacles whose coefficients $${(f_i)_{i=1,\ldots, m}}$$ ( f i ) i = 1 , ... , m depend on $${(u_j)_{j=1,\ldots,m}}$$ ( u j ) j = 1 , ... , m . From the probabilistic point of view, this system is related to optimal stochastic switching problem when the noise is driven by a Lévy process. The switching costs depend on (t, x). As a by-product of the main result we obtain that the value function of the switching problem is continuous and unique solution of its associated Hamilton-Jacobi-Bellman system of equations. The main tool we used is the notion of systems of reflected BSDEs with oblique reflection driven by a Lévy process. Springer Basel, 2015 Integral-partial differential equations nationallicence Interconnected obstacles nationallicence Viscosity solutions nationallicence Lévy process nationallicence Multi-modes switching nationallicence Reflected backward stochastic differential equations nationallicence Hamadène Said Université du Maine, LMM, Avenue Olivier Messiaen, 72085, Le Mans Cedex 9, France aut Zhao Xuxhe Université du Maine, LMM, Avenue Olivier Messiaen, 72085, Le Mans Cedex 9, France aut Nonlinear Differential Equations and Applications NoDEA Springer Basel 22/6(2015-12-01), 1607-1660 1021-9722 22:6<1607 2015 22 30 https://doi.org/10.1007/s00030-015-0338-x text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00030-015-0338-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Hamadène Said Université du Maine, LMM, Avenue Olivier Messiaen, 72085, Le Mans Cedex 9, France aut NATIONALLICENCE 700 1- Zhao Xuxhe Université du Maine, LMM, Avenue Olivier Messiaen, 72085, Le Mans Cedex 9, France aut NATIONALLICENCE 773 0- Nonlinear Differential Equations and Applications NoDEA Springer Basel 22/6(2015-12-01), 1607-1660 1021-9722 22:6<1607 2015 22 30