L. H. Alvarez and &. P. Salminen, Timing in the presence of directional predictability: optimal stopping of skew Brownian motion, Mathematical Methods of Operations Research, vol.52, issue.53, pp.377-400, 2017.
DOI : 10.1007/BF02214254

T. Appuhamillage, V. Bokil, E. Thomann, E. Waymire, and &. B. Wood, Occupation and local times for Skew Brownian motion with application to dispersion accross an interface, Ann. Appl. Probab, vol.211, pp.183-214, 2011.

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 : 10.1007/978-3-662-21726-9

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

M. Bossy, N. Champagnat, S. Maire, and &. D. Talay, Probabilistic interpretation and random walk on spheres algorithms for the Poisson-Boltzmann equation in molecular dynamics, ESAIM: Mathematical Modelling and Numerical Analysis, vol.127, issue.5, pp.997-1048, 2010.
DOI : 10.1063/1.2803189

URL : https://hal.archives-ouvertes.fr/inria-00459411

M. Decamps, M. Goovaerts, and &. W. Schoutens, Self exciting threshold interest rates models, Int. J. Theor. Appl. Finance, vol.97, pp.1093-1122, 2006.
DOI : 10.2139/ssrn.642961

A. P. Dempster, N. M. Laird, and &. B. Rubin, Maximum Likelihood from Incomplete Data via the EM Algorithm, Journal of the Royal Statistical Society. Series B (Methodological), vol.39, issue.1, pp.1-38, 1977.

D. Florens, Estimation of the diffusion coefficient from crossings, Statistical Inference for Stochastic Processes, vol.1, issue.2, pp.175-195, 1998.
DOI : 10.1023/A:1009927813898

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

URL : http://doi.org/10.1214/aop/1176994472

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

K. Itô and &. H. Mckean-jr, Diffusion processes and their sample paths, 1974.

J. Jacod, Une generalisation des semimaritingales : Les processus admettant un processus a accroissements independants tangent, Lecture Notes in Math, vol.XXV, issue.3, pp.91-118, 1984.
DOI : 10.1007/BF00531754

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. Keilson and &. J. Wellner, Oscillating Brownian motion, Journal of Applied Probability, vol.7, issue.02, pp.300-310, 1978.
DOI : 10.1090/S0002-9947-1958-0094863-X

URL : http://www.stat.washington.edu/jaw/JAW-papers/jaw-keilson.JAP-78.pdf

J. Gall, 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 : 10.1215/kjm/1250523691

J. Gall, One ??? dimensional stochastic differential equations involving the local times of the unknown process, In: Stochastic Analysis and Applications. Lecture Notes in Mathematics, vol.52, issue.53, pp.51-82, 1985.
DOI : 10.1215/kjm/1250523691

A. Lejay and &. P. Pigato, A Threshold Model for Local Volatility: Evidence of Leverage and Mean Reversion Effects on Historical Data, SSRN Electronic Journal, 2018.
DOI : 10.2139/ssrn.3101666

URL : https://hal.archives-ouvertes.fr/hal-01669082

A. Lejay and &. P. Pigato, Maximum likelihood drift estimation for a threshold diffusion, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01731566

A. Lejay and &. P. Pigato, Statistical estimation of the Oscillating Brownian Motion, Bernoulli, vol.24, issue.4B, pp.3568-3602, 2018.
DOI : 10.3150/17-BEJ969

URL : https://hal.archives-ouvertes.fr/hal-01430794

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, Estimation of the biais parameter of the Skew Random Walk and application to the Skew Brownian Motion, Statistical Inference for Stochastic Processes, pp.10-1007, 2018.

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, 2012.
DOI : 10.1016/j.jcp.2012.07.011

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

A. Lejay and &. G. Pichot, Simulating diffusion processes in discontinuous media: Benchmark tests, Journal of Computational Physics, vol.314, pp.348-413, 2016.
DOI : 10.1016/j.jcp.2016.03.003

URL : https://hal.archives-ouvertes.fr/hal-01003853

A. Lejay, E. Mordecki, and &. S. Torres, Is a Brownian motion skew? Scand, J. Stat, vol.412, pp.346-364, 2014.
DOI : 10.1111/sjos.12033

D. Lépingle, Un schéma d'Euler pour équations différentielles stochastiques réfléchies, C. R. Acad. Sci. Paris Sér. I Math, vol.3166, pp.601-605, 1993.

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

G. J. Mclachlan and &. T. Krishnan, The EM algorithm and extensions, Probability and Statistics, pp.10-1002, 2008.

O. Ovaskainen and &. S. Cornell, Biased movement at a boundary and conditional occupancy times for diffusion processes, J. Appl. Probab, vol.403, pp.557-580, 2003.
DOI : 10.1239/jap/1059060888

N. I. Portenko, Diffusion Processes with Generalized Drift Coefficients, Theory of Probability & Its Applications, vol.24, issue.1, pp.62-77, 1979.
DOI : 10.1137/1124005

D. Rossello, Arbitrage in skew Brownian motion models, Insurance: Mathematics and Economics, vol.50, issue.1, pp.50-56, 2012.
DOI : 10.1016/j.insmatheco.2011.10.004

D. Spivakovsakaya, A. Heemink, and &. E. Deleersnijder, The backward ??to method for the Lagrangian simulation of transport processes with large space variations of the diffusivity, Ocean Science, vol.3, issue.4, pp.525-535, 2007.
DOI : 10.5194/os-3-525-2007

D. Thomson, W. Physick, and &. R. Maryon, Treatment of Interfaces in Random Walk Dispersion Models, Journal of Applied Meteorology, vol.36, issue.9, pp.1284-1295, 1997.
DOI : 10.1175/1520-0450(1997)036<1284:TOIIRW>2.0.CO;2

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