To join me

Ongoing responsabilities

• Head of the team probability and statistics, Institut Élie Cartan de Lorraine (Nancy, France).
• Editor of the Séminaire de Probabilités, with Catherine Donati-Martin and Alain Rouault.
• Editor of Mathematics and Computers in Simulation.
• Leader of the GDR TRAG on rough paths.
• Member of the board of AMIES.
• Member of the executive board of LUE-Impact projet digitrust.

Some softwares

• currency (LaTeX): consistent formatting of currencies and amounts [Github, CTAN].
• exitbm (C): Simulate random variables related to the first exit time and position of the Brownian motion from simple domains, namely intervals, squares and rectangles [Gforge].

Publications

2019

• Antoine Lejay and Paolo Pigato, A threshold model for local volatility: evidence of leverage and mean reversion effects on historical data, International Journal of Theoretical and Applied Finance (2019) [Hal:hal-01669082, arXiv:1712.08329].

2018

• {Book edited} Catherine Donati-Martin, Antoine Lejay and Alain Rouault, Séminaire de Probabilités XLIX, Lecture Notes in Mathematics, vol. 2215, Springer-Verlag (2018) [Hal:hal-01931202, DOI:10.1007/978-3-319-92420-5].
• {Preprint} Antoine Lejay, Lionel Lenôtre and Géraldine Pichot, An exponential timestepping algorithm for diffusion with discontinuous coefficients (2018), Preprint [Hal:hal-01806465].
• {Preprint} Antoine Lejay and Paolo Pigato, Maximum likelihood drift estimation for a threshold diffusion (2018), Preprint [Hal:hal-01731566, arXiv:1803.05408].
• {Preprint} Antoine Brault and Antoine Lejay, The non-linear sewing lemma II: Lipscthiz continuous formulation (2018), Preprint [Hal:hal-01839202].
• Antoine Brault and Antoine Lejay, The non-linear sewing lemma I: weak formulation, Electronic Journal of Probability (2018) [Hal:hal-01716945].
• {Preprint} Samia Haraketi, Ezedine Haoula and Antoine Lejay, Measurable sub-Riemannian geometry on the lifted Sierpinski gasket to the Heisenberg group (2018), Preprint [Hal:hal-01927134].
• Antoine Lejay, The Girsanov theorem without (so much) stochastic analysis. In: Séminaire de probabilités XLIX, Lecture Notes in Mathematics, Catherine Donati-Martin, Antoine Lejay and Alain Rouault, 2215, Springer-Verlag, 329-361 (2018) [Hal:hal-01498129, DOI:10.1007/978-3-319-92420-5_8].
• Antoine Lejay, Ernesto Modecki and Soledad Torres, Two consistent estimators for the Skew Brownian motion, ESAIM Probab. Stat. (2018) [Hal:hal-01492853].
• Antoine Lejay and Paolo Pigato, Statistical estimation of the Oscillating Brownian Motion, Bernoulli, 24:(4B), 3568-3602 (2018) [Hal:hal-01430794, DOI:10.3150/17-BEJ969, arXiv:1701.02129].
• Laure Coutin and Antoine Lejay, Sensitivity of rough differential equations: an approach through the Omega lemma, Journal of Differential Equations, 264:(6), 3899-3917 (2018) [Hal:hal-00875670, DOI:10.1016/j.jde.2017.11.03].
• Antoine Lejay, Estimation of the biais parameter of the Skew Random Walk and application to the Skew Brownian motion, Statistical Inference for Stochastic Processes, 21:(3), 539-551 (2018) [Hal:hal-01319319, DOI:10.1007/s11203-017-9161-9].
• Antoine Lejay, A Monte Carlo estimation of the mean residence time in cells surrounded by thin layers, Mathematics and Computers in Simulation, 143C, 65-77 (2018) [Hal:hal-01216471, DOI:10.1016/j.matcom.2017.05.008].

2017

• {Technical report} Antoine Lejay and Paolo Pigato, Data and methods for "A threshold model for local volatility: evidence of leverage and mean reversion effects on historical data", INRIA, Technical report RT-0494 (2017) [Hal:hal-01668975].
• {Preprint} Antoine Lejay, Lionel Lenôtre and Géraldine Pichot, Analytic expressions of the solutions of advection-diffusion problems in 1D with discontinuous coefficients (2017), Preprint [Hal:hal-01644270].
• Madalina Deaconu, Antoine Lejay and Khaled Salhi, Approximation of CVaR minimization for hedging under exponential-Lévy models, Journal of Computational and Applied Mathematics, 326C, 138-158 (2017) [Hal:hal-01461215, DOI:10.1016/j.cam.2017.05.005].
• Arturo Kohatsu-Higa, Antoine Lejay and Kazuhiro Yasuda, Weak rate of convergence of the Euler-Maruyama scheme for stochastic differential equations with non-regular drift, Journal of Computational and Applied Mathematics, 326C, 138-158 (2017) [Hal:hal-00840211, DOI:10.1016/j.cam.2017.05.015].

2016

• {Book edited} Catherine Donati-Martin, Antoine Lejay and Alain Rouault, Séminaire de Probabilités XLVIII, Lecture Notes in Mathematics, vol. 2168, Springer-Verlag (2016) [Hal:hal-01403845, DOI:10.1007/978-3-319-44465-9].
• Antoine Lejay and Géraldine Pichot, Simulating Diffusion Processes in Discontinuous Media: Benchmark Tests, Journal of Computational Physics, 314, 348-413 (2016) [Hal:hal-01003853, DOI:10.1016/j.jcp.2016.03.003, MR:3484940, Zbl:1284.65007].
• Khaled Salhi, Nicolas Champagnat, Madalina Deaconu, Antoine Lejay and Nicolas Navet, Regime switching model for financial data: empirical risk analysis, Physica A, 461, 148-157 (2016) [Hal:hal-01095299, DOI:10.1016/j.physa.2016.05.002].
• Antoine Lejay, The snapping out Brownian motion, Annals of Applied Probability, 26:(3), 1727-1742 (2016) [Hal:hal-00781447, DOI:10.1214/15-AAP1131, arXiv:1606.0823].

2015

• {Book edited} Catherine Donati-Martin, Antoine Lejay and Alain Rouault, In Memoriam Marc Yor - Séminaire de Probabilités XLVII, Lecture Notes in Mathematics, vol. 2137, Springer-Verlag (2015) [Hal:hal-01200589, DOI:10.1007/978-3-319-18585-9, MR:3381858, Zbl:1327.60016].
• {Research Report} Antoine Lejay, Lionel Lenôtre and Géraldine Pichot, One-dimensional skew diffusions: explicit expressions of densities and resolvent kernel, Research Report (2015) [Hal:hal-01194187].
• {Research Report} Antoine Lejay, Estimation of the mean residence time in cells surrounded by semi-permeable membranes by a Monte Carlo method, Inria, Research Report RR-8709 (2015) [Hal:hal-01140960].

2014

• {Book edited} Catherine Donati-Martin, Antoine Lejay and Alain Rouault, Séminaire de Probabilités XLVI, Lecture Notes in Mathematics, vol. 2123, Springer-Verlag (2014) [Hal:hal-01109973, DOI:10.1007/978-3-319-11970-0, MR:3307672, Zbl:1305.60008].
• Stanislas Larnier, Rafael Almar, Rodrigo Cienfuegos and Antoine Lejay, On the use of the Radon transform to estimate longshore currents from video imagery, Journal of Coastal Research, SI 70, 23-28 (2014) [Hal:hal-00917807, DOI:10.2112/SI70-005.1].
• Laure Coutin and Antoine Lejay, Perturbed linear rough differential equations, Annales Mathématiques Blaise Pascal, 20:(2), 103-150 (2014) [Hal:hal-00722900, MR:3248224, Zbl:1322.60084, http://ambp.cedram.org/ambp-bin/item?id=AMBP_2014__21_1_103_0].
• {Research Report} Antoine Lejay, Ernesto Mordecki and Soledad Torres, Numerical approximation of Backward Stochastic Differential Equations with jumps, Inria, Research Report RR-8595 (2014) [Hal:inria-00357992].
• Antoine Lejay, Soledad Torres and Ernesto Mordecki, Is a Brownian motion skew?, Scandinavian Journal of Statistics, 4:(2), 346-364 (2014) [Hal:inria-00544442, DOI:10.1111/sjos.12033, MR:3207175].

2013

• Stanislas Larnier, Rafael Almar, Rodrigo Cienfuegos and Antoine Lejay, Détection de courants marins côtiers à partir de séquences vidéo, ESAIM Proceedings and Survey, 45, 359-368 (2013) [Hal:hal-00868401, DOI:10.1051/proc/201445037, MR:3451848, Zbl:1335.9401].
• {Book edited} Catherine Donati-Martin, Antoine Lejay and Alain Rouault, Séminaire de Probabilités XLV, Lecture Notes in Mathematics, vol. 2078, Springer-Verlag (2013) [Hal:hal-00849019, DOI:10.1007/978-3-319-00321-4, MR:3202581, Zbl:1270.60005].
• {Proceedings} Antoine Lejay, Monte Carlo simulations in media with interfaces. In: Interplay of Theory and Numerics for Deterministic and Stochastic Homogenization, Oberwolfach Reports, Guillaume Bal, Björn Engquist, Claude Le Bris and Houman Owhadi, 14/2013, 28-30 (2013) [Hal:hal-00819900, DOI:10.4171/OWR/2013/14]. Proceedings of Interplay of Theory and Numerics for Deterministic and Stochastic Homogenization, Oberwolfach, Germany, 2013.
• Antoine Lejay and Sylvain Maire, New Monte Carlo schemes for simulating diffusions in discontinuous media, Journal of Computational and Applied Mathematics, 245, 97-116 (2013) [Hal:hal-00689581, DOI:10.1016/j.cam.2012.12.013, MR:3016238].

2012

• Antoine Lejay and Géraldine Pichot, Simulating diffusion processes in discontinuous media: a numerical scheme with constant time steps, Journal of Computational Physics, 231:(21), 7299-7314 (2012) [Hal:hal-00649170, DOI:10.1016/j.jcp.2012.07.011, MR:2969713].
• Antoine Lejay and Victor Reutenauer, A variance reduction technique using a quantized Brownian motion as a control variate, J. Comput. Finance, 16:(2), 61-84 (2012) [Hal:inria-00393749].
• Antoine Lejay, Global solutions to rough differential equations with unbounded vector fields. In: Séminaire de probabilités XLIV, Lecture Notes in Mathematics, 2046, Springer-Verlag, 215-246 (2012) [Hal:hal-00724872, DOI:10.1007/978-3-642-27461-9_11, MR:2953350, Zbl:1254.60059].
• {Proceedings} Antoine Lejay, Perturbation of linear rough differential equations and applications. In: Rough Paths and PDEs, Oberwolfach Reports, Dan Crisan, Peter Friz and Massimiliano Gubinelli, 41/2012, 29-30 (2012) [DOI:10.4171/OWR/2012/41]. Proceedings of Rough Paths and PDEs, Oberwolfach, Germany, 2012.
• Antoine Lejay, Trajectoires rugueuses, Matapli, 98, 119-134 (2012) [Hal:hal-00701211, MR:3236290].
• {Proceedings} Arturo Kohatsu-Higa, Antoine Lejay and Kazuhiro Yasuda, On Weak Approximation of Stochastic Differential Equations with Discontinuous Drift Coeffcient. In: RIMS Kôkyûroku, C. Hara, 1788, 94-106 (2012) [Hal:hal-00670123]. Proceedings of Mathematical Economics, Kyoto, Japan, 2012.
• {Book edited} Catherine Donati-Martin, Antoine Lejay and Alain Rouault, Séminaire de Probabilités XLIV, Lecture Notes in Mathematics, vol. 2046, Springer-Verlag (2012) [Hal:hal-00724872, DOI:10.1007/978-3-642-27461-9, MR:2920527, Zbl:1244.60005].

2011

• Antoine Lejay, Simulation of a stochastic process in a discontinuous layered medium, Electronic Communications in Probability, 16, 764-774 (2011) [Hal:inria-00583127, DOI:10.1214/ECP.v16-1686, MR:2861440, Zbl:1243.60062].
• {Book edited} Catherine Donati-Martin, Antoine Lejay and Alain Rouault, Séminaire de Probabilités XLIII, Lecture Notes in Mathematics, vol. 2006, Springer-Verlag (2011) [Hal:inria-00541922, DOI:10.1007/978-3-642-15217-7, MR:2663709].
• {Technical report} Antoine Lejay, exitbm: a library for simulating Brownian motion's exit times and positions from simple domains, INRIA, Technical report RT-0402 (2011) [Hal:inria-00561409].
• {Proceedings} Jocelyne Erhel, Antoine Lejay and Géraldine Pichot, Comparison of some lagrangian schemes for the simulation of diffusion in discontinuous media. In: Proceedings MAMERN11: 4th International Conference on Approximation Methods and Numerical Modelling in Environment and Natural Resources, B. Amaziane, D. Barrera, H. Mraoui, M.L. Rodríguez and D. Sbibih, 319-322 (2011).

2010

• Antoine Lejay, Controlled differential equations as Young integrals: A simple approach, Journal of Differential Equations, 249, 1777-1798 (2010) [Hal:inria-00402397, DOI:10.1016/j.jde.2010.05.006, MR:2679003, Zbl:1216.34058].
• Antoine Lejay and Sylvain Maire, Simulating diffusions with piecewise constant coefficients using a kinetic approximation, Comput. Methods Appl. Mech. Engrg., 199:(29-32), 2014-2023 (2010) [Hal:inria-00358003, DOI:10.1016/j.cma.2010.03.002, MR:2654005].
• Samih Zein, Antoine Lejay and Madalina Deaconu, An Efficient Algorithm to Simulate a Brownian Motion Over Irregular Domains, Communications in Computational Physics, 8:(4), 901-916 (2010) [Hal:inria-00444056, DOI:10.4208/cicp.240209.031209a, MR:2673769].
• Madalina Deaconu and Antoine Lejay, Simulation of a diffusion process using the importance sampling paradigm, Ann. Appl. Probab., 20:(4), 1389-1424 (2010) [Hal:inria-00126339, DOI:10.1214/09-AAP659].

2009

• Antoine Lejay, Yet another introduction to rough paths. In: Séminaire de probabilités XLII, Lecture Notes in Mathematics, 1979, Springer-Verlag, 1-101 (2009) [Hal:inria-00107460, DOI:10.1007/978-3-642-01763-6_1, MR:2599204].
• Antoine Lejay, On rough differential equations, Electron. J. Probab., 14:(12), 341-364 (2009) [Hal:inria-00278246, DOI:10.1214/EJP.v14-613, MR:2480544].
• {Proceedings} Antoine Lejay, Monte Carlo methods for discontinuous media. In: Proceedings of the 3^rd international conference on approximation methods and numerical modelling in environment and natural resources MAMERN09, Pau, France, June 8-11, 2009, B. Amaziane, D. Barrera, M.A. Fortes, M.J. Ibáñez, M. Odunlami, A. Palomares, M. Pasadas, M.L. Rodríguez and D. Sbibih, 2, 591-596 (2009) [Hal:inria-00393738].
• {Misc} Antoine Lejay, A short introduction to rough paths: outline and selected bibliography (2009) [Hal:inria-00419931]. Bibliography related to a lecture on rough paths given in Kiev in 2009.

2008

• Antoine Lejay and Sylvain Maire, Computing the principal eigenelements of some linear operators using a branching Monte Carlo method, J. Comput. Phys., 227:(23), 9794-9806 (2008) [Hal:inria-00151884, DOI:10.1016/j.jcp.2008.07.018, MR:2469034, Zbl:1157.65303].
• Jean Jacod, Antoine Lejay and Denis Talay, Estimation of the Brownian dimension of a continuous Itô process, Bernoulli, 14:(2), 469-498 (2008) [Hal:inria-143541, DOI:10.3150/07-BEJ6190, MR:2544098, Zbl:1155.62059].
• Antoine Lejay, Stochastic Differential Equations driven by processes generated by divergence form operators II. Convergence results, ESAIM Probab. Stat., 12, 387-411 (2008) [Hal:inria-00092427, DOI:10.1051/ps:2007040, MR:2437716, Zbl:1185.60061].
• {Proceedings} Madalina Deaconu and Antoine Lejay, Simulation of exit times and positions for Brownian motions and Diffusions. In: Sixth International Congress on Industrial Applied Mathematics, 7, 1081401-1081402 (2008) [Hal:inria-00348693, DOI:10.1002/pamm.200700564]. Proceedings of Sixth International Congress on Industrial Applied Mathematics (ICIAM07) and GAMM Annual Meeting, Zürich 2007, Zürich, 2007.

2007

• Pierre Étoré and Antoine Lejay, A Donsker theorem to simulate one-dimensional processes with measurable coefficients, ESAIM Probab. Stat., 11, 301-326 (2007) [Hal:inria-00077851, DOI:10.1051/ps:2007021, MR:2339295].
• Antoine Lejay and Sylvain Maire, Computing the principal eigenvalue of the Laplace operator by a stochastic method, Math. Comput. Simulation, 73:(3), 351-363 (2007) [Hal:inria-00092408, DOI:10.1016/j.matcom.2006.06.011, MR:2289255, Zbl:1110.65105].
• {Proceedings} Antoine Lejay, Rough paths. An introduction using classical analysis. In: Numerical Analysis and Applied Mathematics, American Institute of Physics Proceedings, T.E. Simos, G. Psihoyios and Ch. Tsitouras, 937, American Institute of Physics, 339-342 (2007) [Hal:inria-00200339]. Proceedings of International Conference on Numerical Analysis and Applied Mathematics (ICNAAM 2007), Corfou, Greece, 2007.
• {Habilitation} Antoine Lejay, Contributions à la théorie des processus engendrés par des opérateurs sous forme divergence, aux méthodes de Monte Carlo et à la théorie des trajectoires rugueuses, Habilitation, Université Henri Poincaré, Nancy, France 2007.

2006

• Antoine Lejay, On the constructions of the Skew Brownian motion, Probab. Surv., 3, 413-466 (2006) [Hal:inria-00000785, DOI:10.1214/154957807000000013, MR:2280299].
• Antoine Lejay, Stochastic Differential Equations driven by processes generated by divergence form operators I. A Wong-Zakai theorem, ESAIM Probab. Stat., 10, 356-379 (2006) [Hal:inria-00092426, DOI:10.1051/ps:2006015, MR:2247926, Zbl:1181.60085].
• Massimilano Gubinelli, Antoine Lejay and Samy Tindel, Young integrals and SPDEs, Potential Anal., 25:(4), 307-326 (2006) [Hal:inria-00092425, DOI:10.1007/s11118-006-9013-5, MR:2253080, Zbl:1103.60062, arXiv:math.PR/0407294].
• Antoine Lejay and Nicolas Victoir, On (p,q)-rough paths, J. Differential Equations, 225:(1), 103-133 (2006) [Hal:inria-00092420, DOI:10.1016/j.jde.2006.01.018, MR:2228694, Zbl:1097.60048].
• Madalina Deaconu and Antoine Lejay, A random walk on rectangles algorithm, Methodol. Comput. Appl. Probab., 8:(1), 135-151 (2006) [Hal:inria-00092424, DOI:10.1007/s11009-006-7292-3, MR:2253080, Zbl:1104.60046].
• Antoine Lejay and Miguel Martinez, A scheme for simulating one-dimensional diffusion processes with discontinuous coefficients, Ann. Appl. Probab., 16:(1), 107-139 (2006) [Hal:inria-00000410, DOI:10.1214/105051605000000656, MR:2209338, Zbl:1094.60056, arXiv:math.PR/0603214].
• Antoine Lejay and Terry Lyons, On the importance of the Lévy area for systems controlled by converging stochastic processes. Application to homogenization. In: New Trends in Potential Theory, Conference Proceedings, Bucharest, September 2002 and 2003, D. Bakry, L. Beznea, Gh. Bucur and M. Röckner, The Theta Foundation, 63-84 (2006) [Hal:inria-00092419, MR:2243956].
• {Proceedings} Antoine Lejay, A probabilistic interpretation of the transmission conditions using the Skew Brownian motion. In: Multiscale Problems and Asymptotic Analysis, Gakuto International Series Math. Sci., A. Damlamian, D. Lukkassen, A. Meidell and A. Piatnitski, 195-206 (2006) [Hal:inria-00092418, MR:2233179]. Proceedings of Midnight Sun Narvik conference, Narvik, Norvège, 2004.

2005

• Laure Coutin and Antoine Lejay, Semi-martingales and rough paths theory, Electron. J. Probab., 10:(23), 761-785 (2005) [Hal:inria-00000411, DOI:10.1214/EJP.v10-162, MR:2164030, Zbl:1109.60035].

2004

• Antoine Lejay, A Probabilistic Representation of the Solution of some Quasi-Linear PDE with a Divergence-Form Operator. Application to Existence of Weak Solutions of FBSDE, Stochastic Proces. Appl., 110:(1), 145-176 (2004) [Hal:inria-00001228, DOI:10.1016/j.spa.2003.09.012, MR:2052140, Zbl:1075.6007].
• {Proceedings} Antoine Lejay, Monte Carlo methods for fissured porous media. A gridless approach. In: Monte Carlo Methods Appl., 10, 385-392 (2004) [Hal:inria-00102181, DOI:10.1515/mcma.2004.10.3-4.385, MR:2105066, Zbl:1109.76378]. Proceedings of IV IMACS Seminar on Monte Carlo Methods, Berlin, 2003.

2003

• Antoine Lejay, An introduction to rough paths. In: Séminaire de probabilités XXXVII, Lecture Notes in Mathematics, 1832, Springer-Verlag, 1-59 (2003) [Hal:inria-00102184, DOI:10.1007/978-3-540-40004-2_1, MR:2053040, Zbl:1041.60051].
• Antoine Lejay, Simulating a diffusion on a graph. Application to reservoir engineering, Monte Carlo Methods Appl., 9:(3), 241-256 (2003) [Hal:inria-00092428, DOI:10.1163/156939603322729003, MR:2009371].

2002

• Leonid Pastur and Antoine Lejay, Matrices aléatoires. Statistique asymptotique des valeurs propres. In: Séminaire de probabilités XXXVI, Lecture Notes in Mathematics, 1801, Springer-Verlag, 135-164 (2002) [Hal:inria-00102375, DOI:10.1007/978-3-540-36107-7_2, MR:1971583, Zbl:pre02046375].
• Antoine Lejay, On the convergence of stochastic integrals driven by processes converging on account of a homogenization property, Electron. J. Probab., 7:(18), 1-18 (2002) [Hal:inria-00093190, DOI:10.1214/EJP.v7-117, MR:1943891].
• Fabien Campillo and Antoine Lejay, A Monte Carlo method without grid for a fractured porous domain model, Monte Carlo Methods Appl., 8:(2), 129-148 (2002) [Hal:inria-00072590, DOI:10.1515/mcma.2002.8.2.129, MR:1916913].
• Antoine Lejay, BSDE driven by Dirichlet Process and Semi-linear Parabolic PDE. Application to Homogenization, Stochastic Proces. Appl., 97:(1), 1-39 (2002) [Hal:inria-00001229, DOI:10.1016/S0304-4149(01)00124-7, MR:1870718, Zbl:1058.60045].

2001

• Antoine Lejay, On the decomposition of excursions measures of processes whose generators have diffusion coefficients discontinuous at one point, Markov Process. Related Fields, 8:(1), 117-126 (2001) [Hal:inria-00001230, MR:1897608, Zbl:997.60085].
• Antoine Lejay, A Probabilistic Approach of the Homogenization of Divergence-Form Operators in Periodic Media, Asymptot. Anal., 28:(2), 151-162 (2001) [Hal:inria-00001219, MR:1869029].
• Antoine Lejay, Homogenization of divergence-form operators with lower-order terms in random media, Probab. Theory Related Fields, 120:(2), 255-276 (2001) [Hal:inria-00001220, DOI:10.1007/s004400100135, MR:1841330].
• {Proceedings} Antoine Lejay, Weak solution of semi-linear PDE, BSDE and homogenization. In: Monte Carlo Methods Appl., 7, 265-272 (2001) [Hal:inria-00101706, DOI:10.1515/mcma.2001.7.3-4.265, MR:1834783, Zbl:986.35016]. Proceedings of Monte Carlo 2000, 2000.
• {Proceedings} Fabien Campillo and Antoine Lejay, A Monte Carlo Method to Compute the exchange coefficient in the double porosity model. In: Monte Carlo Methods Appl., 7, 65-72 (2001) [Hal:inria-00101707, DOI:10.1515/mcma.2001.7.1-2.65, MR:1828197]. Proceedings of Monte Carlo 2000, 2000.

2000

• {PhD} Antoine Lejay, Méthodes probabilistes pour l'homogénéisation des opérateurs sous forme-divergence: cas linéaires et semi-linéaires, PhD, Université de Provence, Marseille, France 2000.