The PDF file you selected should load here if your Web browser has a PDF reader plug-in installed (for example, a recent version of Adobe Acrobat Reader).

Alternatively, you can also download the PDF file directly to your computer, from where it can be opened using a PDF reader. To download the PDF, click the Download link below.

If you would like more information about how to print, save, and work with PDFs, Highwire Press provides a helpful Frequently Asked Questions about PDFs.

Download this PDF file Fullscreen Fullscreen Off

References

  1. A. Bensoussan, J.L. Lions, and G. Papanicolaou. Asymptotic Analysis for Periodic Structures. North-Holland, 1978. Math Review 82h:35001.
  2. S.N. Ethier and T.G. Kurtz. Markov Processes, Characterization and Convergence. Wiley, 1986. Math Review 88a:60130.
  3. J. Jacod and A.N. Shiryaev. Limit Theorems for Stochastic Processes. Springer-Verlag, 1987. Math Review 89k:60044.
  4. I. Karatzas and S.E. Shreve. Brownian Motion and Stochastic Calculus. Springer-Verlag, 2 edition, 1991. Math Review 92h:60127.
  5. T.G. Kurtz and P. Protter. Weak convergence of stochastic integrals and differential equations. In D. Talay and L. Tubaro, editors, Probabilistic Models for Nonlinear Partial Differential Equations, Montecatini Terme, 1995, vol. 1629 of Lecture Notes in Mathematics, pp. 1—41. Springer-Verlag, 1996. Math Review 98h:60073.
  6. J. L. Lebowitz and H. Rost. The Einstein relation for the displacement of a test particle in a random environment. Stochastic Process. Appl., 54:183—196, 1994. Math Review 97b:60171.
  7. A. Lejay. Homogenization of divergence-form operators with lower-order terms in random media. Probab. Theory Related Fields, 120(2):255—276, 2001. <DOI: 10.1007/s004400100135>. Math Review 2002g:35023.
  8. A. Lejay. A probabilistic approach of the homogenization of divergence-form operators in periodic media. Asymptot. Anal., 28(2):151—162, 2001. Math Review 1 869 029.
  9. A. Lejay. An introduction to rough paths. In Séminaire de Probabilités XXXVII, Lecture Notes in Mathematics. Springer-Verlag, 2003. To appear. MR number not available.
  10. A. Lejay and T.J. Lyons. On the importance of the Lévy area for systems controlled by converging stochastic processes. Application to homogenization. In preparation, 2002. MR number not available.
  11. T.J. Lyons. Differential equations driven by rough signals. Rev. Mat. Iberoamericana, 14(2):215—310, 1998. Math Review 2000c:60089.
  12. T. Lyons and Z. Qian. System Control and Rough Paths. Oxford Mathematical Monographs. Oxford University Press, 2002. MR number not available.
  13. S. Olla. Homogenization of diffusion processes in random fields. Cours de l'École doctorale de l'École Polytechnique (Palaiseau, France), 1994. <www.cmap.polytechnique.fr/~olla/pubolla.html>. MR number not available.
  14. É. Pardoux. Homogenization of linear and semilinear second order PDEs with periodic coefficients: a probabilistic approach. J. Funct. Anal., 167(2):498—520, 1999. <DOI: 10.1006/jfan.1999.3441>. Math Review 2000j:60079.
  15. É. Pardoux and A.Y. Veretennikov. Averaging of backward SDEs, with application to semi-linear PDEs. Stochastics, 60(3—4):255—270, 1997. Math Review 98d:60125.
  16. É. Pardoux and A.Y. Veretennikov. On Poisson equation and diffusion approximation I. Ann. Probab., 29(3):1061—1085, 2001. Math Review 1872736.
  17. É. Pardoux and A.Y. Veretennikov. On poisson equation and diffusion approximation II. To appear in Ann. Probab., 2002. MR number not available.
  18. R.G. Pinsky. Second order elliptic operators with periodic coefficients: criticality theory, perturbations, and positive harmonic functions. J. Funct. Anal., 129(1):80—107, 1995. Math Review 96b:35038.
  19. R.G. Pinsky. Positive Harmonic Functions and Diffusion. Cambridge University Press, 1996. Math Review 96m:60179.
  20. I. Szyszkowski. Weak convergence of stochastic integrals. Theory of Probab. App., 41(4):810—814, 1997. Math Review 2000c:60082.


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.