Probabilistic interpretation of a system of semi-linear parabolic partial differential equations

Etienne Pardoux; Frédéric Pradeilles; Zusheng Rao

Annales de l'I.H.P. Probabilités et statistiques (1997)

  • Volume: 33, Issue: 4, page 467-490
  • ISSN: 0246-0203

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Pardoux, Etienne, Pradeilles, Frédéric, and Rao, Zusheng. "Probabilistic interpretation of a system of semi-linear parabolic partial differential equations." Annales de l'I.H.P. Probabilités et statistiques 33.4 (1997): 467-490. <http://eudml.org/doc/77578>.

@article{Pardoux1997,
author = {Pardoux, Etienne, Pradeilles, Frédéric, Rao, Zusheng},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {backward stochastic differential equations; parabolic partial differential equations; viscosity solutions},
language = {eng},
number = {4},
pages = {467-490},
publisher = {Gauthier-Villars},
title = {Probabilistic interpretation of a system of semi-linear parabolic partial differential equations},
url = {http://eudml.org/doc/77578},
volume = {33},
year = {1997},
}

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
PB - Gauthier-Villars
VL - 33
IS - 4
SP - 467
EP - 490
LA - eng
KW - backward stochastic differential equations; parabolic partial differential equations; viscosity solutions
UR - http://eudml.org/doc/77578
ER -

References

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  1. [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. Zbl0878.60036MR1436432
  2. [2] K. Bichteler, J-B. Gravereau and J. Jacod, Malliavin Calculus for Processes with Jumps, Stoch. Monographs, Vol. 2, Gordon, 1987. Zbl0706.60057MR1008471
  3. [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. Zbl0755.35015MR1118699
  4. [4] E.B. Dynkin, Superprocesses and partial differential equations, Ann. Probab., Vol. 21, 1993, pp. 1185-1262. Zbl0806.60066MR1235414
  5. [5] W.H. Fleming and H.M. Soner, Controlled Markov processes and viscosity solutions, Applications of Mathematics, Vol. 25, Springer, 1993. Zbl0773.60070MR1199811
  6. [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. Zbl0742.35022MR1116855
  7. [7] J. Jacod, A General Theorem of Representation for Martingales, Proceed. of Symposia in Pure Math., Vol. 31, 1977, pp. 37-53. Zbl0362.60068MR443074
  8. [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. Zbl0045.07002MR45333
  9. [9] H.P. Mckean, A class of Markov processes associated with nonlinear parabolic equations, Proc. Nat. Acad. Sci., Vol. 56, 1966, pp. 1907-1911. Zbl0149.13501MR221595
  10. [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. [11] D. Nualart and E. Pardoux, Stochastic Calculus with Anticipating integrands, Prob. Theory and Rel. Fields, Vol. 78, 1988, pp. 535-581. Zbl0629.60061MR950346
  12. [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. Zbl0893.60036MR1652339
  13. [13] E. Pardoux and S. Peng, Adapted solution of a backward stochastic differential equation, System and Control Letters, Vol. 14, 1990, pp. 55-61. Zbl0692.93064MR1037747
  14. [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. Zbl0766.60079
  15. [15] S. Peng, A generalized dynamic programming principle and Hamilton-Jacobi-Bellman equations, Stochastics and Stochastics Reports, Vol. 38, 1992, pp. 119-134. Zbl0756.49015MR1274898
  16. [16] S. Peng, Probabilistic interpretation for systems of quasilinear parabolic partial differential equations, Stochastics and Stochastics Reports, Vol. 37, 1991, pp. 61-74. Zbl0739.60060MR1149116
  17. [17] F. Pradeilles, Wave Front Propagation in Systems of Reaction-Diffusion Equations, Ann. Probab., to appear. Zbl0933.35098
  18. [18] P. Protter, Stochatic integration and differential equations, Springer1990. Zbl0694.60047MR1037262
  19. [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, Springer1991. Zbl0732.60114MR1108185

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