Abstract, Monte Carlo Methods and Applications, vol.22, issue.3, 2015. ,
DOI : 10.1515/mcma-2016-0109
Asymptotic error distribution for the ninomiya-victoir scheme in the commutative case, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01390897
Asymptotics for the normalized error of the ninomiya-victoir scheme, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01259915
High order discretization schemes for the CIR process: Application to affine term structure and Heston models, Mathematics of Computation, vol.79, issue.269, pp.209-237, 2010. ,
DOI : 10.1090/S0025-5718-09-02252-2
URL : https://hal.archives-ouvertes.fr/hal-00143723
Affine diffusions and related processes: simulation, theory and applications, 2015. ,
DOI : 10.1007/978-3-319-05221-2
Approximation of Markov semigroups in total variation distance, Electronic Journal of Probability, vol.21, p.44, 2016. ,
DOI : 10.1214/16-EJP4079
URL : https://hal.archives-ouvertes.fr/hal-01110015
The law of the Euler scheme for stochastic differential equations, Probability Theory and Related Fields, vol.8, issue.1, pp.43-60, 1996. ,
DOI : 10.1007/BF01303802
URL : https://hal.archives-ouvertes.fr/inria-00074016
The Law of the Euler Scheme for Stochastic Differential Equations: II. Convergence Rate of the Density, Monte Carlo Methods and Applications, vol.2, issue.2, pp.93-128, 1996. ,
DOI : 10.1515/mcma.1996.2.2.93
URL : https://hal.archives-ouvertes.fr/inria-00074016
Cubature on Wiener Space: Pathwise Convergence, Applied Mathematics & Optimization, vol.35, issue.3, pp.261-278, 2013. ,
DOI : 10.1007/s00245-012-9187-8
URL : http://arxiv.org/pdf/1304.4623
Central limit theorem for the multilevel Monte Carlo Euler method, The Annals of Applied Probability, vol.25, issue.1, pp.211-234, 2015. ,
DOI : 10.1214/13-AAP993
URL : https://hal.archives-ouvertes.fr/hal-00693191
Retrospective exact simulation of diffusion sample paths with applications, Bernoulli, vol.12, issue.6, pp.1077-1098, 2006. ,
DOI : 10.3150/bj/1165269151
The pricing of options and corporate liabilities. The journal of political economy, pp.637-654, 1973. ,
Numerical methods for ordinary differential equations, 2008. ,
DOI : 10.1002/0470868279
The maximum rate of convergence of discrete approximations for stochastic differential equations, Stochastic differential systems (Proc. IFIP-WG 7/1 Working Conf, pp.162-171, 1978. ,
DOI : 10.1007/BFb0004007
A theory of the term structure of interest rates, Econometrica: Journal of the Econometric Society, pp.385-407, 1985. ,
On the Acceleration of the Multi-Level Monte Carlo Method, Journal of Applied Probability, vol.52, issue.02, pp.307-322, 2015. ,
DOI : 10.1007/s10543-010-0276-2
Fondements de l'analyse moderne. Traduit de l'anglais par D. Huet. Avant-propos de G, 1963. ,
Liens entre équations différentielles stochastiques et ordinaires, Ann. Inst. H. Poincaré Sect. B (N.S.), vol.13, issue.2, pp.99-125, 1977. ,
Efficient Monte Carlo Simulation of Security Prices, The Annals of Applied Probability, vol.5, issue.4, pp.897-905, 1995. ,
DOI : 10.1214/aoap/1177004598
Sixth order methods of kusuoka approximation, Preprint UTMS, 2006. ,
Random Generation of Stochastic Area Integrals, SIAM Journal on Applied Mathematics, vol.54, issue.4, pp.1132-1146, 1994. ,
DOI : 10.1137/S0036139992235706
Multilevel Monte Carlo Path Simulation, Operations Research, vol.56, issue.3, pp.607-617, 2008. ,
DOI : 10.1287/opre.1070.0496
Antithetic multilevel Monte Carlo estimation for multi-dimensional SDEs without L??vy area simulation, The Annals of Applied Probability, vol.24, issue.4, pp.1585-1620, 2014. ,
DOI : 10.1214/13-AAP957
URL : http://arxiv.org/abs/1202.6283
Euler scheme and tempered distributions. Stochastic Process, Appl, vol.116, issue.6, pp.877-904, 2006. ,
DOI : 10.1016/j.spa.2005.11.011
URL : http://doi.org/10.1016/j.spa.2005.11.011
Efficient and Practical Implementations of Cubature on Wiener Space, Stochastic analysis 2010, pp.73-111, 2011. ,
DOI : 10.1007/978-3-642-15358-7_5
Solving ordinary differential equations. I, 1993. ,
DOI : 10.1007/978-3-662-12607-3
A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options, Review of Financial Studies, vol.6, issue.2, pp.327-343, 1993. ,
DOI : 10.1093/rfs/6.2.327
Term Structure Movements and Pricing Interest Rate Contingent Claims, The Journal of Finance, vol.10, issue.5, pp.1011-1029, 1986. ,
DOI : 10.1111/j.1540-6261.1986.tb02528.x
Hypoelliptic second order differential equations, Acta Mathematica, vol.119, issue.0, pp.147-171, 1967. ,
DOI : 10.1007/BF02392081
On continuous conditional Gaussian martingales and stable convergence in law, Séminaire de Probabilités, XXXI, pp.232-246, 1997. ,
DOI : 10.1007/978-3-662-02514-7
Asymptotic error distributions for the Euler method for stochastic differential equations, The Annals of Probability, vol.26, issue.1, pp.267-307, 1998. ,
DOI : 10.1214/aop/1022855419
The Rate of Convergence for Approximate Solutions of Stochastic Differential Equations, Tokyo Journal of Mathematics, vol.12, issue.1, pp.33-48, 1989. ,
DOI : 10.3836/tjm/1270133546
Statistical Romberg extrapolation: A new variance reduction method and applications to option pricing, The Annals of Applied Probability, vol.15, issue.4, pp.2681-2705, 2005. ,
DOI : 10.1214/105051605000000511
URL : https://hal.archives-ouvertes.fr/hal-00693106
Numerical solution of stochastic differential equations, Applications of Mathematics, vol.23, 1992. ,
Wong-Zakai corrections, random evolutions, and simulation schemes for SDEs, Stochastic analysis, pp.331-346, 1991. ,
DOI : 10.1016/b978-0-12-481005-1.50023-5
Approximation of expectation of diffusion process and mathematical finance, Taniguchi Conference on Mathematics Nara '98, pp.147-165, 2001. ,
Approximation of expectation of diffusion processes based on Lie algebra and Malliavin calculus, Advances in mathematical economics, pp.69-83, 2004. ,
DOI : 10.1007/978-4-431-68450-3_4
Multilevel Richardson-Romberg extrapolation, 2014. ,
DOI : 10.2139/ssrn.2539114
URL : https://hal.archives-ouvertes.fr/hal-00920660
Cubature on Wiener space, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.460, issue.2041, pp.169-198, 2004. ,
DOI : 10.1098/rspa.2003.1239
Differential equations driven by rough signals, Revista Matem??tica Iberoamericana, vol.14, issue.2, pp.215-310, 1998. ,
DOI : 10.4171/RMI/240
Stochastic analysis, volume 313 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences, 1997. ,
Approximate integration of stochastic differential equations, Teor. Verojatnost. i Primenen, vol.19, pp.583-588, 1974. ,
A new higher-order weak approximation scheme for??stochastic differential equations and??the??Runge???Kutta method, Finance and Stochastics, vol.8, issue.3???6, pp.415-443, 2009. ,
DOI : 10.1007/s00780-009-0101-4
Weak Approximation of Stochastic Differential Equations and Application to Derivative Pricing, Applied Mathematical Finance, vol.29, issue.2, pp.107-121, 2008. ,
DOI : 10.1016/0020-7225(65)90045-5
A new extrapolation method for weak approximation schemes with applications, The Annals of Applied Probability, vol.22, issue.3, pp.1008-1045, 2012. ,
DOI : 10.1214/11-AAP774
Multi-step Richardson-Romberg Extrapolation: Remarks on Variance Control and Complexity, Monte Carlo Methods and Applications, vol.13, issue.1, pp.37-70, 2007. ,
DOI : 10.1515/MCMA.2007.003
Continuous-time stochastic control and optimization with financial applications, volume 61 of Stochastic Modelling and Applied Probability, 2009. ,
On a Taylor formula for a class of Itô processes, Probab. Math. Statist, vol.3, issue.1, pp.37-51, 1982. ,
Numerical approximation of partial differential equations, 1994. ,
On stable sequences of events. Sankhy¯ a Ser, pp.293-302, 1963. ,
Continuous martingales and Brownian motion, of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences, 1999. ,
DOI : 10.1007/978-3-662-06400-9
Expansion of the global error for numerical schemes solving stochastic differential equations, Stochastic Analysis and Applications, vol.20, issue.4, pp.483-509, 1990. ,
DOI : 10.1080/07362999008809220
URL : https://hal.archives-ouvertes.fr/inria-00075490
Ordinary differential equations and dynamical systems, Graduate Studies in Mathematics, vol.140, 2012. ,
DOI : 10.1090/gsm/140
An equilibrium characterization of the term structure, Journal of Financial Economics, vol.5, issue.2, pp.177-188, 1977. ,
DOI : 10.1016/0304-405X(77)90016-2
Asymptotic error for the Milstein scheme for SDEs driven by continuous semimartingales, The Annals of Applied Probability, vol.15, issue.4, pp.2706-2738, 2005. ,
DOI : 10.1214/105051605000000520