@article{AIHPB_1997__33_4_467_0, author = {Pardoux, Etienne and Pradeilles, Fr\'ed\'eric and Rao, Zusheng}, title = {Probabilistic interpretation of a system of semi-linear parabolic partial differential equations}, journal = {Annales de l'I.H.P. Probabilit\'es et statistiques}, pages = {467--490}, publisher = {Gauthier-Villars}, volume = {33}, number = {4}, year = {1997}, mrnumber = {1465798}, zbl = {0891.60054}, language = {en}, url = {http://archive.numdam.org/item/AIHPB_1997__33_4_467_0/} }
TY - JOUR AU - Pardoux, Etienne AU - Pradeilles, Frédéric AU - Rao, Zusheng TI - Probabilistic interpretation of a system of semi-linear parabolic partial differential equations JO - Annales de l'I.H.P. Probabilités et statistiques PY - 1997 SP - 467 EP - 490 VL - 33 IS - 4 PB - Gauthier-Villars UR - http://archive.numdam.org/item/AIHPB_1997__33_4_467_0/ LA - en ID - AIHPB_1997__33_4_467_0 ER -
%0 Journal Article %A Pardoux, Etienne %A Pradeilles, Frédéric %A Rao, Zusheng %T Probabilistic interpretation of a system of semi-linear parabolic partial differential equations %J Annales de l'I.H.P. Probabilités et statistiques %D 1997 %P 467-490 %V 33 %N 4 %I Gauthier-Villars %U http://archive.numdam.org/item/AIHPB_1997__33_4_467_0/ %G en %F AIHPB_1997__33_4_467_0
Pardoux, Etienne; Pradeilles, Frédéric; Rao, Zusheng. Probabilistic interpretation of a system of semi-linear parabolic partial differential equations. Annales de l'I.H.P. Probabilités et statistiques, Tome 33 (1997) no. 4, pp. 467-490. http://archive.numdam.org/item/AIHPB_1997__33_4_467_0/
[1] BSDE's and integro-partial differential equations, Stochastics and Stochastics Reports, Vol. 60, 1997, pp. 57-83. | MR | Zbl
, and ,[2] Malliavin Calculus for Processes with Jumps, Stoch. Monographs, Vol. 2, Gordon, 1987. | MR | Zbl
, and ,[3] User's guide to viscosity solutions of second order partial differential equations, Bull AMS, Vol. 27, 1992, pp. 1-67. | MR | Zbl
, and ,[4] Superprocesses and partial differential equations, Ann. Probab., Vol. 21, 1993, pp. 1185-1262. | MR | Zbl
,[5] Controlled Markov processes and viscosity solutions, Applications of Mathematics, Vol. 25, Springer, 1993. | MR | Zbl
and ,[6] Viscosity solutions for monotone systems of second-order elliptic PDEs, Commun. in Partial Differential equations, Vol. 16-17, 1991, pp. 1095-1128. | MR | Zbl
and ,[7] A General Theorem of Representation for Martingales, Proceed. of Symposia in Pure Math., Vol. 31, 1977, pp. 37-53. | MR | Zbl
,[8] On some connections between probability theory and differential and integral equations, Proc. 2nd Berkeley Symposium on Math. Stat. and Probability, Univ. of Calif. Press, 1951, pp. 189-215. | MR | Zbl
,[9] A class of Markov processes associated with nonlinear parabolic equations, Proc. Nat. Acad. Sci., Vol. 56, 1966, pp. 1907-1911. | MR | Zbl
,[10] On the probability-theoretic solution of systems of elliptic and parabolic equations, Theory Probab. and Applic., Vol. 23, 1978, pp. 820-824.
,[11] Stochastic Calculus with Anticipating integrands, Prob. Theory and Rel. Fields, Vol. 78, 1988, pp. 535-581. | MR | Zbl
and ,[12] Backward stochastic differential equations and viscosity solutions of systems of semilinear parabolic and elliptic PDEs of second order, Proc. Geilo Conf., 1996, to appear. | MR | Zbl
,[13] Adapted solution of a backward stochastic differential equation, System and Control Letters, Vol. 14, 1990, pp. 55-61. | MR | Zbl
and ,[14] Backward stochastic differential equations and quasilinear parabolic partial differential equations, in Stochastic Partial Differential Equations and their Applications, B. L. Rozovskii & R. B. Sowers eds., LNCIS, Vol. 176, Springer, 1992, pp. 200-217. | Zbl
and ,[15] A generalized dynamic programming principle and Hamilton-Jacobi-Bellman equations, Stochastics and Stochastics Reports, Vol. 38, 1992, pp. 119-134. | MR | Zbl
,[16] Probabilistic interpretation for systems of quasilinear parabolic partial differential equations, Stochastics and Stochastics Reports, Vol. 37, 1991, pp. 61-74. | MR | Zbl
,[17] Wave Front Propagation in Systems of Reaction-Diffusion Equations, Ann. Probab., to appear.
,[18] Stochatic integration and differential equations, Springer 1990. | MR | Zbl
,[19] Topics in propagation of chaos, in Ecole d'été de Probabilité de St Flour XIX, Lecture Notes in Mathematics, Vol. 1464, Springer 1991. | MR | Zbl
,