caa a22 4500 467953481 CHVBK 20180405193745.0 cr unu---uuuuu 170328e20050201xx s 000 0 eng 10.1007/s11118-003-6457-8 doi (NATIONALLICENCE)springer-10.1007/s11118-003-6457-8 (NATIONALLICENCE)springer-10.1007/s11118-004-6457-3 Backward Stochastic Differential Equations Associated to a Symmetric Markov Process [Elektronische Daten] [V. Bally, E. Pardoux, L. Stoica] We consider a second order semi-elliptic differential operator L with measurable coefficients, in divergence form, and the semilinear parabolic system of PDE's $$(\partial _{t}+L)u(t,x)+f(t,x,u,\nabla u\sigma )=0,\quad \forall 0\leqslant t\leqslant T,$$ $$u(T,x)=\Phi (x).$$ We solve this system in the framework of Dirichlet spaces and employ the symmetric Markov process of infinitesimal operator L in order to obtain a precised version of the solution u by solving the corresponding system of backward stochastic differential equations. This precised version verifies pointwise the so called "mild equation”, which is equivalent to the above PDE. As a technical ingrediend we prove a representation theorem for arbitrary martingales which generalises a result of Fukushima for martingale additive functionals. The nonlinear term f satisfies a monotonicity condition with respect to u and a Lipschitz condition with respect to ∇u. Springer, 2005 backward stochastic differential equations nationallicence symmetric Markov processes nationallicence divergence form semilinear parabolic partial differential equations nationallicence Bally V. Université du Maine, Faculté des Sciences, Département de Mathématiques, Laboratoire de Statistique et Processus, Av. Olivier Messiaen, 72085, Le Mans cedex 9, France aut Pardoux E. LATP/CMI, Université de Provence, 39, rue F. Joliot Curie, 13 453, Marseille cedex 13, France aut Stoica L. Université de Bucarest, Faculté de Mathématiques, Str. Academiei 14, ro70109, Bucarest, Roumanie aut Potential Analysis Kluwer Academic Publishers 22/1(2005-02-01), 17-60 0926-2601 22:1<17 2005 22 11118 https://doi.org/10.1007/s11118-003-6457-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11118-003-6457-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bally V. Université du Maine, Faculté des Sciences, Département de Mathématiques, Laboratoire de Statistique et Processus, Av. Olivier Messiaen, 72085, Le Mans cedex 9, France aut NATIONALLICENCE 700 1- Pardoux E. LATP/CMI, Université de Provence, 39, rue F. Joliot Curie, 13 453, Marseille cedex 13, France aut NATIONALLICENCE 700 1- Stoica L. Université de Bucarest, Faculté de Mathématiques, Str. Academiei 14, ro70109, Bucarest, Roumanie aut NATIONALLICENCE 773 0- Potential Analysis Kluwer Academic Publishers 22/1(2005-02-01), 17-60 0926-2601 22:1<17 2005 22 11118 NATIONALLICENCE 700 1- Bally V. Faculté des Sciences, Département de Mathématiques, Laboratoire de Statistique et Processus, Université du Maine, Av. Olivier Messiaen, 72085, Le Mans cedex 9, France aut NATIONALLICENCE 700 1- Pardoux E. Université de Provence, LATP/CMI, 39, rue F. Joliot Curie, 13 453, Marseille cedex 13, France aut NATIONALLICENCE 700 1- Stoica L. Faculté de Mathématiques, Université de Bucarest, Str. Academiei 14, ro70109, Bucarest, Roumanie aut NATIONALLICENCE 856 40 https://doi.org/10.1007/s11118-004-6457-3 text/html Onlinezugriff via DOI Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE NATIONALLICENCE NL-springer