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References
- R.F. Bass and Z.-Q. Chen. One-dimensional Stochastic Differential Equations with Singular and Degenerate Coefficients. Sankhya 67 (2005), 19-45. Math. Review number not available.
- L. Breiman. Probability. Addison-Wesley Publishing Company, Reading, Mass.-London-Don Mills, Ont. (1968), ix+421 pp. Math. Review MR0229267
- H. Brézis. Analyse fonctionnelle. Masson. (1983), xiv+234 pp. Math. Review 85a:46001
- M. Decamps, A. De Schepper and M. Goovaerts. Applications of delta-function pertubation to the pricing of derivative securities. Physica A 342:3-4 (2004), 677-692. Math. Review number not available.
- 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), x+534pp. Math. Review 88a:60130
- J.M. Harrison and L.A. Shepp. On skew Brownian Motion. The Annals of Probability 9 (1981), 309-313. Math. Review 82j:60144
- K. It and H.P. McKean. Diffusion Processes and Their Sample Paths. Springer, Berlin. (1974), xv+321 pp. Math. Review MR0345224
- P.E. Kloeden and E. Platen. Numerical Solution of Stochastic Differential Equations. Springer, Berlin (1992), xxxvi+632 pp. Math. Review 94b:60069
- O.A. Ladyzenskaja, V.A. Solonnikov and N.N. Ural'ceva. Linear and Quasilinear Equations of Parabolic Type. Translations of Mathematical Monographs, American Mathematical Society. 23 (1968), xi+648 pp. Math. Review MR0241822
- O.A. Ladyzenskaja, V.J. Rivkind and N.N. Ural'ceva. The classical solvability of diffraction problems. Trudy Mat. Inst. Steklov 92 (1966), 116-146. Math. Review MR0211050
- A. Lejay. Méthodes probabilistes pour l'homogénéisation des opérateurs sous forme divergence: cas linéaires et semi-linéaires. PhD thesis, Université de Provence, Marseille, France, 2000.
- A. Lejay and M. Martinez. A scheme for simulating one-dimensional diffusion processes with discontinuous coefficients. Preprint submitted to The Annals of Applied Probability. (2006).
- J.F. Le Gall. One-dimensional stochastic differential equations involving the local time of the unknown process. Springer, Stochastic Analysis and Applications, Lect. Notes in Math. 1095 (1985) 51-82. Math. Review 86g:60071
- M. Martinez. Interprtations probabilistes d'oprateurs sous forme divergence et analyse de mthodes numriques probabilistes associes. PhD thesis, Universit de Provence, Marseille, France, 2004.
- M. Martinez and D. Talay. Discrétisation d'équations différentielles stochastiques unidimensionnelles à générateur sous forme divergence avec coefficient discontinu. C.R. Acad. Sci. Paris 342:1 (2006), 51-56. Math. Review number not available.
- D. Revuz and M. Yor. Continuous Martingale and Brownian Motion. Springer, Heidelberg (1991), x+533 pp. Math. Review 92d:60053
- D. W. Stroock. Aronson's Estimate for Elliptic Operators in Divergence Form. Springer , Lecture Notes in Mathematics, Seminaire de Probabilités XXII 1321 (1982), 316-347. Math. Review number not available.
- J.B. Walsh. A Diffusion with a Discontinuous Local Time. Société Mathématique de France, Astérisque 52-53 (1978), 37-45. Math. Review number not available.

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