Free Access
Issue
ESAIM: M2AN
Volume 44, Number 5, September-October 2010
Special Issue on Probabilistic methods and their applications
Page(s) 997 - 1048
DOI https://doi.org/10.1051/m2an/2010050
Published online 26 August 2010
  1. D.G. Aronson, Bounds for the fundamental solution of a parabolic equation. Bull. Amer. Math. Soc. 73 (1967) 890–896. [CrossRef] [MathSciNet] [Google Scholar]
  2. N.A. Baker, D. Sept, M.J. Holst and J.A. McCammon, The adaptive multilevel finite element solution of the Poisson-Boltzmann equation on massively parallel computers. IBM J. Res. Dev. 45 (2001) 427–437. [CrossRef] [Google Scholar]
  3. N.A. Baker, D. Bashford and D.A. Case, Implicit solvent electrostatics in biomolecular simulation, in New algorithms for macromolecular simulation, Lect. Notes Comput. Sci. Eng. 49, Springer, Berlin (2005) 263–295. [Google Scholar]
  4. A.N. Borodin and P. Salminen, Handbook of Brownian motion-facts and formulae. Probability and its Applications, 2nd edition, Birkhäuser Verlag, Basel (2002). [Google Scholar]
  5. H. Brezis, Analyse fonctionnelle : Théorie et applications. Collection Mathématiques Appliquées pour la Maîtrise, Masson, Paris (1983). [Google Scholar]
  6. R. Dautray and J.-L. Lions, Evolution problems II, Mathematical analysis and numerical methods for science and technology 6. Springer-Verlag, Berlin (1993). [Google Scholar]
  7. S.N. Ethier and T.G. Kurtz, Markov processes – Characterization and convergence. Wiley Series in Probability and Mathematical Statistics, Probability and Mathematical Statistics, John Wiley & Sons Inc., New York (1986). [Google Scholar]
  8. M. Fukushima, Y. Ōshima and M. Takeda, Dirichlet forms and symmetric Markov processes, de Gruyter Studies in Mathematics 19. Walter de Gruyter & Co., Berlin (1994). [Google Scholar]
  9. D. Gilbarg and N.S. Trudinger, Elliptic partial differential equations of second order. Classics in Mathematics, Reprint of the 1998 edition, Springer-Verlag, Berlin (2001). [Google Scholar]
  10. N. Ikeda and S. Watanabe, Stochastic differential equations and diffusion processes, North-Holland Mathematical Library 24. Second edition, North-Holland Publishing Co., Amsterdam (1989). [Google Scholar]
  11. I. Karatzas and S.E. Shreve, Brownian motion and stochastic calculus, Graduate Texts in Mathematics 113. Second edition, Springer-Verlag, New York (1991). [Google Scholar]
  12. O.A. Ladyzhenskaya and N.N. Ural'tseva, Linear and quasilinear elliptic equations. Academic Press, New York (1968). [Google Scholar]
  13. B. Lapeyre, É. Pardoux and R. Sentis, Introduction to Monte-Carlo methods for transport and diffusion equations, Oxford Texts in Applied and Engineering Mathematics 6. Oxford University Press, Oxford (2003). [Google Scholar]
  14. J.-F. Le Gall, One-dimensional stochastic differential equations involving the local times of the unknown process, in Stochastic analysis and applications (Swansea, 1983), Lecture Notes Math. 1095, Springer, Berlin (1984) 51–82. [Google Scholar]
  15. A. Lejay, Méthodes probabilistes pour l'homogénéisation des opérateurs sous forme divergence : Cas linéaires et semi-linéaires. Ph.D. Thesis, Université de Provence, Marseille, France (2000). [Google Scholar]
  16. A. Lejay and S. Maire, Simulating diffusions with piecewise constant coefficients using a kinetic approximation. Comput. Meth. Appl. Mech. Eng. 199 (2010) 2014–2023. [CrossRef] [Google Scholar]
  17. A. Lejay and M. Martinez, A scheme for simulating one-dimensional diffusion processes with discontinuous coefficients. Ann. Appl. Probab. 16 (2006) 107–139. [CrossRef] [MathSciNet] [Google Scholar]
  18. N. Limić, Markov jump processes approximating a nonsymmetric generalized diffusion. Preprint, arXiv:0804.0848v4 (2008). [Google Scholar]
  19. S. Maire, Réduction de variance pour l'intégration numérique et pour le calcul critique en transport neutronique. Ph.D. Thesis, Université de Toulon et du Var, France (2001). [Google Scholar]
  20. S. Maire and D. Talay, On a Monte Carlo method for neutron transport criticality computations. IMA J. Numer. Anal. 26 (2006) 657–685. [CrossRef] [MathSciNet] [Google Scholar]
  21. M. Martinez, Interprétations probabilistes d'opérateurs sous forme divergence et analyse des méthodes numériques probabilistes associées. Ph.D. Thesis, Université de Provence, Marseille, France (2004). [Google Scholar]
  22. M. Martinez and D. Talay, Discrétisation d'équations différentielles stochastiques unidimensionnelles à générateur sous forme divergence avec coefficient discontinu. C. R. Math. Acad. Sci. Paris 342 (2006) 51–56. [CrossRef] [MathSciNet] [Google Scholar]
  23. M. Mascagni and N.A. Simonov, Monte Carlo methods for calculating some physical properties of large molecules. SIAM J. Sci. Comput. 26 (2004) 339–357. [CrossRef] [MathSciNet] [Google Scholar]
  24. N.I. Portenko, Diffusion processes with a generalized drift coefficient. Teor. Veroyatnost. i Primenen. 24 (1979) 62–77. [MathSciNet] [Google Scholar]
  25. N.I. Portenko, Stochastic differential equations with a generalized drift vector. Teor. Veroyatnost. i Primenen. 24 (1979) 332–347. [MathSciNet] [Google Scholar]
  26. P.E. Protter, Stochastic integration and differential equations – Second edition, Version 2.1, Stochastic Modelling and Applied Probability 21. Corrected third printing, Springer-Verlag, Berlin (2005). [Google Scholar]
  27. D. Revuz and M. Yor, Continuous martingales and Brownian motion, Grundlehren der Mathematischen Wissenschaften 293. Springer-Verlag, Berlin (1991). [Google Scholar]
  28. L.C.G. Rogers and D. Williams, Foundations, Diffusions, Markov processes, and martingales 1. Reprint of the second edition (1994), Cambridge Mathematical Library, Cambridge University Press, Cambridge (2000). [Google Scholar]
  29. L.C.G. Rogers and D. Williams, Itô calculus, Diffusions, Markov processes, and martingales 2. Reprint of the second edition (1994), Cambridge Mathematical Library, Cambridge University Press, Cambridge (2000). [Google Scholar]
  30. A. Rozkosz and L. Słomiński, Extended convergence of Dirichlet processes. Stochastics Stochastics Rep. 65 (1998) 79–109. [MathSciNet] [Google Scholar]
  31. K.K. Sabelfeld, Monte Carlo methods in boundary value problems. Springer Series in Computational Physics, Springer-Verlag, Berlin (1991). [Google Scholar]
  32. K.K. Sabelfeld and D. Talay, Integral formulation of the boundary value problems and the method of random walk on spheres. Monte Carlo Meth. Appl. 1 (1995) 1–34. [CrossRef] [Google Scholar]
  33. N.A. Simonov, Walk-on-spheres algorithm for solving boundary-value problems with continuity flux conditions, in Monte Carlo and quasi-Monte Carlo methods 2006, Springer, Berlin (2008) 633–643. [Google Scholar]
  34. N.A. Simonov, M. Mascagni and M.O. Fenley, Monte Carlo-based linear Poisson-Boltzmann approach makes accurate salt-dependent solvation free energy predictions possible. J. Chem. Phys. 127 (2007) 185105. [CrossRef] [PubMed] [Google Scholar]
  35. D.W. Stroock, Diffusion semigroups corresponding to uniformly elliptic divergence form operators, in Séminaire de Probabilités, XXII, Lecture Notes in Math. 1321, Springer, Berlin (1988) 316–347. [Google Scholar]
  36. D.W. Stroock and S.R.S. Varadhan, Multidimensional diffusion processes, Grundlehren der Mathematischen Wissenschaften 233. Springer-Verlag, Berlin (1979). [Google Scholar]

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