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Original Articles

Homogenization of Multivalued Partial Differential Equations via Reflected Backward Stochastic Differential Equations

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Pages 81-98 | Published online: 16 Aug 2006

References

  • Bally , V. , Caballero , M.E. and Fernandez , B. Reflected BSDE's, PDE's and variational inequality. Prépublication de luniversité Paris VI, Laboratoire de probabilités
  • Barles , G. and Lesigne , E. 1997 . “ SDE, BSDE and PDE ” . In Bakward Stochastic Differential Equations , Pitman Research Notes in Math. Series 364 Edited by: El Karoui , N. and Mazliak , L. Singapore : Longman .
  • Barbu , V. and Precupanu , T. 1986 . “ Convexity and Optimization in Banach Spaces ” . In Mathematics and Its Applications , East European Series Singapore
  • Bensoussan , A. , Lions , J.L. and Papanicolaou , G. 1978 . Asymptotic Analysis for Periodic Structure North Holland , , Singapore
  • Billingsley , P. 1968 . Convergence of Probability Measures Willey , , Singapore
  • Buckdahn , R. , Hu , Y. and Peng , S. 1999 . Probabilistic approach to homogenization of viscosity solutions of parabolic PDEs . Nonlinear Differential Equations Appl. , 6 : 395 – 411 . [CROSSREF]
  • Cépa , E . 1994 . Equations Différentielles Multivoques, Thése de doctorat de l'université d'Orleans
  • El Karoui , N. , Peng , S. and Quenez , M.C. 1997 . Backward stochastic differential equations in finance . Math. Finance , 7 : 1 – 71 . [CROSSREF]
  • Freidlin , M. 1964 . The Dirichlet problem for an equation with periodic coefficients depending on a small parameter . Teor. Veoj. i Primenen , 9 : 133 – 139 .
  • Gaudron , G. and Pardoux , E. 2001 . EDSR, convergence en loi et homogénéisation d'EDP paraboliques semi-linéaires . Ann. Inst. Henri Poincaré , 37 ( 1 ) : 1 – 42 . [CROSSREF]
  • Hamadene , S. and Lepeltier , J.P. 1999 . Zero-sum stochastic differential games and BSDEs . Systems Control Lett. , 24 : 259 – 263 . [CROSSREF]
  • Kurtz , T.G. 1991 . Random time changes and convergence in distribution under the Meyer-Zheng conditions . Ann. Prob. , 19 : 1010 – 1034 .
  • Lejay , A. 2000 . Approche probabiliste de l'homogénéisation des opérateurs sous forme divergence en milieu périodique. Thèse de doctorat, Marseille
  • Meyer , P.A. and Zheng , W.A. 1984 . Tightness criteria for laws of semimartingales . Ann. Inst. Henri Poincaré , 20 : 353 – 372 .
  • Ouknine , Y. 1999 . Reflected BSDE with jumps . Stoch. Stoch. Reports , 65 : 111 – 125 .
  • Ouknine , Y. and Pardoux , E. 1999 . Homogenization of PDE's with non linear boundary condition. To appear in Proc. Conf. Ascona
  • Pardoux , E. 1999 . Homogenization of linear and semilinear second order parabolic PDEs with periodic coefficients: a probabilistic approach . J. Funct. Anal. , 167 : 498 – 520 . [CROSSREF]
  • Pardoux , E. 1998 . “ Backward stochastic differential equations and viscosity solutions of systems of semilinear parabolic and elliptic PDEs of second order ” . In Stochastic Analysis and Related Topics: The Geilo Workshop Edited by: Decreusefond , L. , Gjerde , J. , Oksendal , B. and Ustüunel , A.S. 79 – 127 . Singapore : Birkhäuser .
  • Pardoux , E. and Peng , S. 1990 . Adapted solution of a backward stochastic differential equation . System Control Lett. , 14 : 55 – 61 . [CROSSREF]
  • Pardoux , E. and Rascanu , A. 1998 . Backward SDE's with maximal monotone operator . Stoch. Proc. Appl. , 76 : 191 – 215 . [CROSSREF]
  • Pardoux , E. and Veretennikov , YU.A. 1997 . Averaging of backward SDEs, with application to semi-linear PDEs . Stochastics , 60 : 255 – 270 .

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