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. 
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     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://www.numdam.org/item/AIHPB_1997__33_4_467_0/}
}
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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 | Zbl

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

[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 | Zbl

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

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

[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 | Zbl

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

[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 | Zbl

[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 | Zbl

[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 | Zbl

[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 | Zbl

[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 | Zbl

[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

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

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

[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 | Zbl

[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 | Zbl