D. J. Aldous and G. K. Eagleson, On Mixing and Stability of Limit Theorems, The Annals of Probability, vol.6, issue.2, pp.325-331, 1978.
DOI : 10.1214/aop/1176995577

O. Bardou and M. Martinez, Statistical estimation for reflected skew processes, Statistical Inference for Stochastic Processes, vol.35, issue.1, pp.231-248, 2010.
DOI : 10.1007/s11203-010-9047-6

URL : https://hal.archives-ouvertes.fr/hal-00704352

R. Cantrell and C. Cosner, Diffusion Models for Population Dynamics Incorporating Individual Behavior at Boundaries: Applications to Refuge Design, Theoretical Population Biology, vol.55, issue.2, pp.189-207, 1999.
DOI : 10.1006/tpbi.1998.1397

D. Florens-zmirou, On estimating the diffusion coefficient from discrete observations, J. Appl. Probab, vol.304, pp.790-804, 1993.

E. Fujihara, Y. Kawamura, and Y. Yano, Functional limit theorems for occupation times of Lamperti???s stochastic processes in discrete time, Journal of Mathematics of Kyoto University, vol.47, issue.2, pp.429-440, 2007.
DOI : 10.1215/kjm/1250281054

J. M. Harrison and L. A. Shepp, On Skew Brownian Motion, The Annals of Probability, vol.9, issue.2, pp.309-313, 1981.
DOI : 10.1214/aop/1176994472

R. Höpfner and E. Löcherbach, Limit theorems for null recurrent Markov processes, Mem. Amer. Math. Soc, pp.161-768, 2003.

I. Ibragimov and R. Has-'minskii, Statistical Estimation Asymptotic Theory, 1981.

J. Jacod and A. N. Shiryaev, Limit theorems for stochastic processes, 1987.
DOI : 10.1007/978-3-662-02514-7

J. Jacod, Rates of convergence to the local time of a diffusion, Annales de l'Institut Henri Poincare (B) Probability and Statistics, vol.34, issue.4, pp.505-544, 1998.
DOI : 10.1016/S0246-0203(98)80026-5

J. Jacod, Parametric inference for discretely observed non-ergodic diffusions, Bernoulli, vol.12, issue.3, pp.383-401, 2006.
DOI : 10.3150/bj/1151525127

Y. Kutoyants, Parameter Estimation for Stochastic Processes, 1984.

J. Lamperti, An occupation time theorem for a class of stochastic processes, Transactions of the American Mathematical Society, vol.88, issue.2, pp.380-387, 1958.
DOI : 10.1090/S0002-9947-1958-0094863-X

L. Cam, L. Yang, and G. L. , Asymptotics in statistics, 2000.

L. Gall and J. , One ??? dimensional stochastic differential equations involving the local times of the unknown process, Lecture Notes in Math, vol.52, issue.53, pp.51-82, 1983.
DOI : 10.1512/iumj.1975.24.24047

A. Lejay, On the constructions of the skew Brownian motion, Probability Surveys, vol.3, issue.0, pp.413-466, 2006.
DOI : 10.1214/154957807000000013

URL : https://hal.archives-ouvertes.fr/inria-00000785

A. Lejay and M. Martinez, A scheme for simulating one-dimensional diffusion processes with discontinuous coefficients, The Annals of Applied Probability, vol.16, issue.1, pp.107-139, 2006.
DOI : 10.1214/105051605000000656

URL : https://hal.archives-ouvertes.fr/inria-00000410

A. Lejay and G. Pichot, Simulating diffusion processes in discontinuous media: A numerical scheme with constant time steps, Journal of Computational Physics, vol.231, issue.21, pp.7299-7314, 2012.
DOI : 10.1016/j.jcp.2012.07.011

URL : https://hal.archives-ouvertes.fr/hal-00649170

D. Lépingle, Euler scheme for reflected stochastic differential equations, Mathematics and Computers in Simulation, vol.38, issue.1-3, pp.119-126, 1992.
DOI : 10.1016/0378-4754(93)E0074-F

D. Lépingle, Un schéma d'Euler pour équations différentielles stochastiques réfléchies, C. R. Acad. Sci. Paris Sér. I Math. 316, vol.6, pp.601-605, 1993.

R. Lipster and A. Shiryaev, Statistics of random processes. II. Applications, 2001.

M. Martinez, Interprétations probabilistes d'opérateurs sous forme divergence et analyse de méthodes numériques associées, 2004.

O. Ovaskainen and S. J. Cornell, Biased movement at a boundary and conditional occupancy times for diffusion processes, J. Appl. Probab, vol.403, pp.557-580, 2003.

J. M. Ramirez, E. A. Thomann, E. C. Waymire, R. Haggerty, and B. Wood, A Generalized Taylor???Aris Formula and Skew Diffusion, Multiscale Modeling & Simulation, vol.5, issue.3, pp.786-801, 2006.
DOI : 10.1137/050642770

A. Rényi, On stable sequences of events. Sankhy¯ a Ser, pp.293-302, 1963.

J. Walsh, A diffusion with discontinuous local time, In: Temps locaux, pp.52-53, 1978.

M. Zhang, Calculation of Diffusive Shock Acceleration of Charged Particles by Skew Brownian Motion, The Astrophysical Journal, vol.541, issue.1, pp.428-435, 2000.
DOI : 10.1086/309429

@. Torres and C. Facultad-de-ingeniería, Universidad de Valparaíso; Casilla 123-V; Chile