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BSDE driven by Dirichlet process and semi-linear parabolic PDE. Application to homogenization

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  • Lejay, Antoine

Abstract

Backward stochastic differential equations (BSDE) also gives the weak solution of a semi-linear system of parabolic PDEs with a second-order divergence-form partial differential operator and possibly discontinuous coefficients. This is proved here by approximation. After that, a homogenization result for such a system of semi-linear PDEs is proved using the weak convergence of the solution of the corresponding BSDEs in the S-topology.

Suggested Citation

  • Lejay, Antoine, 2002. "BSDE driven by Dirichlet process and semi-linear parabolic PDE. Application to homogenization," Stochastic Processes and their Applications, Elsevier, vol. 97(1), pages 1-39, January.
    • Handle: RePEc:eee:spapps:v:97:y:2002:i:1:p:1-39
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    References listed on IDEAS

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    1. Rozkosz, Andrzej, 1996. "Stochastic representation of diffusions corresponding to divergence form operators," Stochastic Processes and their Applications, Elsevier, vol. 63(1), pages 11-33, October.
    2. Rozkosz, Andrzej & Slominski, Leszek, 1991. "On existence and stability of weak solutions of multidimensional stochastic differential equations with measurable coefficients," Stochastic Processes and their Applications, Elsevier, vol. 37(2), pages 187-197, April.
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    Cited by:

    1. Maticiuc, Lucian & Răşcanu, Aurel, 2016. "On the continuity of the probabilistic representation of a semilinear Neumann–Dirichlet problem," Stochastic Processes and their Applications, Elsevier, vol. 126(2), pages 572-607.
    2. Xing, Hao & Žitković, Gordan, 2018. "A class of globally solvable Markovian quadratic BSDE systems and applications," LSE Research Online Documents on Economics 73440, London School of Economics and Political Science, LSE Library.
    3. Boufoussi, B. & van Casteren, J., 2004. "An approximation result for a nonlinear Neumann boundary value problem via BSDEs," Stochastic Processes and their Applications, Elsevier, vol. 114(2), pages 331-350, December.
    4. Lejay, Antoine, 2004. "A probabilistic representation of the solution of some quasi-linear PDE with a divergence form operator. Application to existence of weak solutions of FBSDE," Stochastic Processes and their Applications, Elsevier, vol. 110(1), pages 145-176, March.
    5. Gassous, Anouar M. & Răşcanu, Aurel & Rotenstein, Eduard, 2015. "Multivalued backward stochastic differential equations with oblique subgradients," Stochastic Processes and their Applications, Elsevier, vol. 125(8), pages 3170-3195.

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