Homogenization of a semilinear parabolic PDE with locally periodic coefficients: a probabilistic approach

Abdellatif Benchérif-Madani; Étienne Pardoux

ESAIM: Probability and Statistics (2007)

  • Volume: 11, page 385-411
  • ISSN: 1292-8100

Abstract

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In this paper, a singular semi-linear parabolic PDE with locally periodic coefficients is homogenized. We substantially weaken previous assumptions on the coefficients. In particular, we prove new ergodic theorems. We show that in such a weak setting on the coefficients, the proper statement of the homogenization property concerns viscosity solutions, though we need a bounded Lipschitz terminal condition.

How to cite

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Benchérif-Madani, Abdellatif, and Pardoux, Étienne. "Homogenization of a semilinear parabolic PDE with locally periodic coefficients: a probabilistic approach." ESAIM: Probability and Statistics 11 (2007): 385-411. <http://eudml.org/doc/250095>.

@article{Benchérif2007,
abstract = { In this paper, a singular semi-linear parabolic PDE with locally periodic coefficients is homogenized. We substantially weaken previous assumptions on the coefficients. In particular, we prove new ergodic theorems. We show that in such a weak setting on the coefficients, the proper statement of the homogenization property concerns viscosity solutions, though we need a bounded Lipschitz terminal condition. },
author = {Benchérif-Madani, Abdellatif, Pardoux, Étienne},
journal = {ESAIM: Probability and Statistics},
keywords = {Homogenization; nonlinear parabolic PDE; Poisson equation; diffusion approximation; backward SDE.; backward SDE; new ergodic theorems},
language = {eng},
month = {8},
pages = {385-411},
publisher = {EDP Sciences},
title = {Homogenization of a semilinear parabolic PDE with locally periodic coefficients: a probabilistic approach},
url = {http://eudml.org/doc/250095},
volume = {11},
year = {2007},
}

TY - JOUR
AU - Benchérif-Madani, Abdellatif
AU - Pardoux, Étienne
TI - Homogenization of a semilinear parabolic PDE with locally periodic coefficients: a probabilistic approach
JO - ESAIM: Probability and Statistics
DA - 2007/8//
PB - EDP Sciences
VL - 11
SP - 385
EP - 411
AB - In this paper, a singular semi-linear parabolic PDE with locally periodic coefficients is homogenized. We substantially weaken previous assumptions on the coefficients. In particular, we prove new ergodic theorems. We show that in such a weak setting on the coefficients, the proper statement of the homogenization property concerns viscosity solutions, though we need a bounded Lipschitz terminal condition.
LA - eng
KW - Homogenization; nonlinear parabolic PDE; Poisson equation; diffusion approximation; backward SDE.; backward SDE; new ergodic theorems
UR - http://eudml.org/doc/250095
ER -

References

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  10. T. Kurtz, Random time changes and convergence in distribution under the Meyer-Zheng conditions. Ann. Prob.19 (1991) 1010–1034.  
  11. P.A. Meyer and W.A. Zheng, Tightness criteria for laws of semimartingales. Anal. I. H. P.20 (1984) 353–372.  
  12. E. Pardoux, Homogenization of linear and semilinear second order Parabolic PDEs with periodic coefficients: -a probabilistic approach. J. Func. Anal.167 (1999a) 498–520.  
  13. E. Pardoux, BSDEs, weak convergence and homogenization of semilinear PDEs, in Nonlinear analysis, Differential Equations and Control, F.H. Clarke and R.J. Stern Eds., Kluwer Acad. Pub. (1999b) 503–549.  

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