Interpolation and Approximation of Piecewise Smooth Functions, SIAM Journal on Numerical Analysis, vol.43, issue.1, pp.41-57, 2005. ,
DOI : 10.1137/S0036142903426245
URL : https://hal.archives-ouvertes.fr/hal-00018287
Approximation schemes for sdes with discontinuous coefficients, 2006. ,
Stochastic flows of diffeomorphisms for one-dimensional SDE with discontinuous drift, Electronic Communications in Probability, vol.15, issue.0, pp.213-226, 2010. ,
DOI : 10.1214/ECP.v15-1545
On irregular functionals of SDEs and the Euler scheme, Finance Stoch, pp.381-401, 2009. ,
The law of the Euler scheme for stochastic differential equations. I. Convergence rate of the distribution function, Probab. Theory Related Fields The law of the Euler scheme for stochastic differential equations. II. Convergence rate of the density, Monte Carlo Methods Appl, pp.43-60, 1996. ,
URL : https://hal.archives-ouvertes.fr/inria-00074016
On mean numbers of passage times in small balls of discretized It?? processes, Electronic Communications in Probability, vol.14, issue.0, pp.302-316, 2009. ,
DOI : 10.1214/ECP.v14-1479
Weak consistency of the Euler method for numerically solving stochastic differential equations with discontinuous coefficients, Stochastic Process, Appl, vol.76, issue.1, pp.33-44, 1998. ,
An explicit representation of the transition densities of the skew Brownian motion with drift and two semipermeable barriers, Monte Carlo Methods Appl, pp.1-23, 2016. ,
Nonparametric Density Estimation. The L 1 view, 1985. ,
Exact simulation for solutions of one-dimensional stochastic differential equations with discontinuous drift, ESAIM Probab, Stat, vol.18, pp.686-702, 2014. ,
Examples of singular parabolic measures and singular transition probability densities, Duke Math, J, vol.48, issue.4, pp.845-856, 1981. ,
DOI : 10.1215/s0012-7094-81-04846-8
Decomposition of Besov spaces, Indiana Univ, Math. Journ, vol.34, pp.777-799, 1985. ,
DOI : 10.1515/9781400827268.385
Littlewood-Paley theory and the study of function spaces, CBMS-AMS Regional Conf. Ser. 79. Providence, Amer. Math, 1991. ,
DOI : 10.1090/cbms/079
Generalized fractional smoothness and L p -variation of Bsdes with non- Lipschitz terminal condition, Stochastic Proces, Appl, vol.122, pp.2078-2116, 2012. ,
Fractional smoothness and applications in finance, Advanced mathematical methods for finance, pp.313-331, 2011. ,
DOI : 10.1007/978-3-642-18412-3_12
URL : http://arxiv.org/abs/1004.3577
Weak convergence of error processes in discretizations of stochastic integrals and Besov spaces, Bernoulli, vol.15, issue.4, pp.925-954, 2009. ,
DOI : 10.3150/09-BEJ197
Sensitivity Analysis Using It??--Malliavin Calculus and Martingales, and Application to Stochastic Optimal Control, SIAM Journal on Control and Optimization, vol.43, issue.5, pp.1676-1713, 2005. ,
DOI : 10.1137/S0363012902419059
A note on strong solutions of stochastic differential equations with a discontinuous drift coefficient, Journal of Applied Mathematics and Stochastic Analysis, vol.21, issue.2, 2006. ,
DOI : 10.1016/S0304-4149(02)00181-3
Difference methods for stochastic differential equations with discontinuous coefficients, Stochastics, vol.9, issue.2, pp.199-212, 1984. ,
DOI : 10.1007/978-1-4612-6380-7
Numerical solution of stochastic differential equations, Applications of Mathematics, vol.23, 1992. ,
On Weak Approximation of Stochastic Differential Equations with Discontinuous Drift Coefficient, RIMS Kôkyûroku, pp.1788-94, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-00670123
Weak approximations. A Malliavin calculus approach, Mathematics of Computation, vol.70, issue.233, pp.135-172, 2001. ,
DOI : 10.1090/S0025-5718-00-01201-1
Weak error for the Euler scheme approximation of diffusions with non-smooth coefficients, Electronic Journal of Probability, vol.22, issue.0, pp.1604-00771, 2016. ,
DOI : 10.1214/17-EJP53
URL : https://hal.archives-ouvertes.fr/hal-01297066
An Inequality in the Theory of Stochastic Integrals, Theory of Probability & Its Applications, vol.16, issue.3, pp.438-448, 1971. ,
DOI : 10.1137/1116048
H??lder continuity and bounds for fundamental solutions to nondivergence form parabolic equations, Analysis & PDE, vol.8, issue.1, pp.1-32, 2015. ,
DOI : 10.2140/apde.2015.8.1
URL : http://arxiv.org/abs/1310.4600
Approximation from shift-invariant spaces, Constructive Approximation, vol.77, issue.2, pp.141-164, 1995. ,
DOI : 10.1007/978-3-0346-0416-1
Ural'ceva, Linear and Quasilinear Equations of Parabolic Type, 1967. ,
On some non asymptotic bounds for the Euler scheme, Electron, J. Probab, vol.15, issue.53, pp.1645-1681, 2010. ,
A numerical method for SDEs with discontinuous drift, BIT Numerical Mathematics, vol.22, issue.129, pp.151-162, 2016. ,
DOI : 10.1070/SM1974v022n01ABEH001689
URL : http://arxiv.org/abs/1503.08005
One-dimensional parabolic diffraction equations: pointwise estimates and discretization of related stochastic differential equations with weighted local times, Electronic Journal of Probability, vol.17, issue.0, pp.17-1905, 2012. ,
DOI : 10.1214/EJP.v17-1905
URL : https://hal.archives-ouvertes.fr/inria-00607967
Weak Euler Approximation for It?? Diffusion and Jump Processes, Stochastic Analysis and Applications, vol.20, issue.1, pp.549-571, 2015. ,
DOI : 10.1287/moor.22.3.668
Rate of Convergence of the Euler Approximation for Diffusion Processes, Mathematische Nachrichten, vol.20, issue.1, pp.233-239, 1991. ,
DOI : 10.1007/BFb0006577
Strong rate of convergence for the Euler-Maruyama approximation of stochastic differential equations with irregular coefficients, Mathematics of Computation, vol.85, issue.300, pp.1793-1819, 2016. ,
DOI : 10.1090/mcom3042
The Malliavin calculus and related topics, Probability and its Applications, 2006. ,
DOI : 10.1007/978-1-4757-2437-0
Abstract, Advances in Applied Probability, vol.48, issue.A, pp.249-259, 2016. ,
DOI : 10.1214/105051605000000485
Optimality of Euler-type algorithms for approximation of stochastic differential equations with discontinuous coefficients, International Journal of Computer Mathematics, vol.91, issue.7, pp.1461-1479, 2014. ,
DOI : 10.1214/aop/1029867124
Discrete Approximations of Strong Solutions of Reflecting SDEs with Discontinuous Coefficients, Bulletin of the Polish Academy of Sciences Mathematics, vol.57, issue.2, pp.169-180, 2009. ,
DOI : 10.4064/ba57-2-10
Methods of Approximation Theory, VSP, 2005. ,
DOI : 10.1515/9783110195286
A Fourier analysis of the finite-element variational method, Constructive Aspects of Functional Analysis, C.I.M.E, pp.793-840, 1971. ,
ON STRONG SOLUTIONS AND EXPLICIT FORMULAS FOR SOLUTIONS OF STOCHASTIC INTEGRAL EQUATIONS, Mathematics of the USSR-Sbornik, vol.39, issue.3, pp.387-403, 1981. ,
DOI : 10.1070/SM1981v039n03ABEH001522
The Euler scheme with irregular coefficients, The Annals of Probability, vol.30, issue.3, pp.1172-1194, 2002. ,
DOI : 10.1214/aop/1029867124