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, p. 467-490
@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},
     publisher = {Gauthier-Villars},
     volume = {33},
     number = {4},
     year = {1997},
     pages = {467-490},
     zbl = {0891.60054},
     mrnumber = {1465798},
     language = {en},
     url = {http://www.numdam.org/item/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://www.numdam.org/item/AIHPB_1997__33_4_467_0/

[1] G. Barles, R. Buckdahn and E. Pardoux, BSDE's and integro-partial differential equations, Stochastics and Stochastics Reports, Vol. 60, 1997, pp. 57-83. | MR 1436432 | Zbl 0878.60036

[2] K. Bichteler, J-B. Gravereau and J. Jacod, Malliavin Calculus for Processes with Jumps, Stoch. Monographs, Vol. 2, Gordon, 1987. | MR 1008471 | Zbl 0706.60057

[3] M.G. Crandall, H. Ishii and P.-L. Lions, User's guide to viscosity solutions of second order partial differential equations, Bull AMS, Vol. 27, 1992, pp. 1-67. | MR 1118699 | Zbl 0755.35015

[4] E.B. Dynkin, Superprocesses and partial differential equations, Ann. Probab., Vol. 21, 1993, pp. 1185-1262. | MR 1235414 | Zbl 0806.60066

[5] W.H. Fleming and H.M. Soner, Controlled Markov processes and viscosity solutions, Applications of Mathematics, Vol. 25, Springer, 1993. | MR 1199811 | Zbl 0773.60070

[6] H. Ishii and S. Koike, Viscosity solutions for monotone systems of second-order elliptic PDEs, Commun. in Partial Differential equations, Vol. 16-17, 1991, pp. 1095-1128. | MR 1116855 | Zbl 0742.35022

[7] J. Jacod, A General Theorem of Representation for Martingales, Proceed. of Symposia in Pure Math., Vol. 31, 1977, pp. 37-53. | MR 443074 | Zbl 0362.60068

[8] M. Kac, 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 45333 | Zbl 0045.07002

[9] H.P. Mckean, A class of Markov processes associated with nonlinear parabolic equations, Proc. Nat. Acad. Sci., Vol. 56, 1966, pp. 1907-1911. | MR 221595 | Zbl 0149.13501

[10] G.N. Milstein, On the probability-theoretic solution of systems of elliptic and parabolic equations, Theory Probab. and Applic., Vol. 23, 1978, pp. 820-824.

[11] D. Nualart and E. Pardoux, Stochastic Calculus with Anticipating integrands, Prob. Theory and Rel. Fields, Vol. 78, 1988, pp. 535-581. | MR 950346 | Zbl 0629.60061

[12] E. Pardoux, 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 1652339 | Zbl 0893.60036

[13] E. Pardoux and S. Peng, Adapted solution of a backward stochastic differential equation, System and Control Letters, Vol. 14, 1990, pp. 55-61. | MR 1037747 | Zbl 0692.93064

[14] E. Pardoux and S. Peng, 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 0766.60079

[15] S. Peng, A generalized dynamic programming principle and Hamilton-Jacobi-Bellman equations, Stochastics and Stochastics Reports, Vol. 38, 1992, pp. 119-134. | MR 1274898 | Zbl 0756.49015

[16] S. Peng, Probabilistic interpretation for systems of quasilinear parabolic partial differential equations, Stochastics and Stochastics Reports, Vol. 37, 1991, pp. 61-74. | MR 1149116 | Zbl 0739.60060

[17] F. Pradeilles, Wave Front Propagation in Systems of Reaction-Diffusion Equations, Ann. Probab., to appear.

[18] P. Protter, Stochatic integration and differential equations, Springer 1990. | MR 1037262 | Zbl 0694.60047

[19] A.S. Sznitman, Topics in propagation of chaos, in Ecole d'été de Probabilité de St Flour XIX, Lecture Notes in Mathematics, Vol. 1464, Springer 1991. | MR 1108185 | Zbl 0732.60114