2010

Controlled differential equations as Young integrals: A simple approach, Journal of Differential Equations, Antoine Lejay, 249, 1777-1798 (2010) [Hal, Journal].
Simulating diffusions with piecewise constant coefficients using a kinetic approximation, Comput. Methods Appl. Mech. Engrg., Antoine Lejay and Sylvain Maire, 199:29-32, 2014-2023 (2010) [Hal, Journal].
An Efficient Algorithm to Simulate a Brownian Motion Over Irregular Domains, Communications in Computational Physics, Samih Zein, Antoine Lejay and Madalina Deaconu, 8:4, 901-916 (2010) [Hal, Journal].
Simulation of a diffusion process using the importance sampling paradigm, Ann. Appl. Probab., Madalina Deaconu and Antoine Lejay, 20, 1389-1424 (2010) [Hal, Journal].
{Preprint} Global solutions to rough differential equations with unbounded vector fields, Antoine Lejay (2010) [Hal]

2009

{Survey} Yet another introduction to rough paths, Antoine Lejay, In: Séminaire de probabilités XLII, Lecture Notes in Mathematics 1979, Springer-Verlag, 1-101 (2009) [Hal, Journal].
On rough differential equations, Electron. J. Probab., Antoine Lejay, 14:12, 341-364 (2009) [Hal].
{Proc} Monte Carlo methods for discontinuous media, Antoine Lejay, 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, eds: 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].
{Preprint} A variance reduction technique using a quantized Brownian motion as a control variate, Antoine Lejay and Victor Reutenauer (2009) [Hal]
{Unpublished} A short introduction to rough paths: outline and selected bibliography, Antoine Lejay (2009) [Hal].

2008

Computing the first eigenelements of some linear operators using a branching Monte Carlo method, J. Comput. Phys., Antoine Lejay and Sylvain Maire, 227:23, 9794-9806 (2008) [Hal, Journal].
Estimation of the Brownian dimension of a continuous Itô process, Bernoulli, Jean Jacod, Antoine Lejay and Denis Talay, 14:2, 469-498 (2008) [Hal, Journal].
Stochastic Differential Equations driven by processes generated by divergence form operators II. Convergence results, ESAIM Probab. Stat., Antoine Lejay, 12, 387-411 (2008) [Hal, Journal].
{Proc} Simulation of exit times and positions for Brownian motions and Diffusions, PAMM 7:1, 1081401-1081402 (2008) [Sixth International Congress on Industrial Applied Mathematics (ICIAM07) and GAMM Annual Meeting, Zürich 2007, Zürich] [Hal, Journal]
{Preprint} Numerical approximation of Backward Stochastic Differential Eqations with jumps, Antoine Lejay, E. Mordecki and S. Torres (2008) [Hal]

2007

A Donsker theorem to simulate one-dimensional processes with measurable coefficients, ESAIM Probab. Stat., Pierre Étoré and Antoine Lejay, 11, 301-326 (2007) [Hal, Journal].
Computing the principal eigenvalue of the Laplace operator by a stochastic method, Math. Comput. Simulation, Antoine Lejay and Sylvain Maire, 73:3, 351-363 (2007) [Hal, Journal].
{Proc} Rough paths. An introduction using classical analysis, Antoine Lejay, In: Numerical Analysis and Applied Mathematics, eds: T.E. Simos, G. Psihoyios and Ch. Tsitouras, American Institute of Physics Proceedings 937, American Institute of Physics, 339-342 (2007) [International Conference on Numerical Analysis and Applied Mathematics (ICNAAM 2007), Corfou, Greece, 2007] [Hal].
{Habilitation} 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, Antoine Lejay, Université Henri Poincaré, Nancy, France (2007).

2006

{Survey} On the constructions of the Skew Brownian motion, Probab. Surv., Antoine Lejay, 3, 413-466 (2006) [Hal].
Stochastic Differential Equations driven by processes generated by divergence form operators I. A Wong-Zakai theorem, ESAIM Probab. Stat., Antoine Lejay, 10, 356-379 (2006) [Hal, Journal].
Young integrals and SPDEs, Potential Anal., Massimilano Gubinelli, Antoine Lejay and Samy Tindel, 25:4, 307-326 (2006) [Hal, Journal].
On (p,q)-rough paths, J. Differential Equations, Antoine Lejay and Nicolas Victoir, 225:1, 103-133 (2006) [Hal, Journal].
A random walk on rectangles algorithms, Methodol. Comput. Appl. Probab., Madalina Deaconu and Antoine Lejay, 8:1, 135-151 (2006) [Hal, Journal].
A scheme for simulating one-dimensional diffusion processes with discontinuous coefficients, Ann. Appl. Probab., Antoine Lejay and Miguel Martinez, 16:1, 107-139 (2006) [Hal, Journal].
On the importance of the Lévy area for systems controlled by converging stochastic processes. Application to homogenization, Antoine Lejay and Terry Lyons, In: New Trends in Potential Theory, Conference Proceedings, Bucharest, September 2002 and 2003, eds: D. Bakry, L. Beznea, Gh. Bucur and M. Röckner, The Theta Foundation, 63-84 (2006) [Hal].
{Proc} A probabilistic interpretation of the transmission conditions using the Skew Brownian motion, Antoine Lejay, In: Multiscale Problems and Asymptotic Analysis, eds: A. Damlamian, D. Lukkassen, A. Meidell and A. Piatnitski, Gakuto International Series Math. Sci., 195-206 (2006) [Midnight Sun Narvik conference, Narvik, Norvège, 2004] [Hal].

2005

Semi-martingales and rough paths theory, Electron. J. Probab., Laure Coutin and Antoine Lejay, 10:23, 761-785 (2005) [Hal].

2004

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., Antoine Lejay, 110:1, 145-176 (2004) [Hal, Journal].
{Proc} Monte Carlo methods for fissured porous media. A gridless approach, Monte Carlo Methods Appl. 10:3-4, 385-392 [IV IMACS Seminar on Monte Carlo Methods, Berlin, 2003] [Hal]

2003

{Survey} An introduction to rough paths, Antoine Lejay, In: Séminaire de probabilités XXXVII, Lecture Notes in Mathematics 1832, Springer-Verlag, 1-59 (2003) [Hal, Mathscinet, Zbl].
Simulating a diffusion on a graph. Application to reservoir engineering, Monte Carlo Methods Appl., Antoine Lejay, 9:3, 241-256 (2003) [Hal].

2002

{Survey} Matrices aléatoires. Statistique asymptotique des valeurs propres, Leonid Pastur and Antoine Lejay, In: Séminaire de probabilités XXXVI, Lecture Notes in Mathematics 1801, Springer-Verlag, 135-164 (2002) [Hal, Mathscinet, Zbl].
On the convergence of stochastic integrals driven by processes converging on account of a homogenization property, Electron. J. Probab., Antoine Lejay, 7:18, 1-18 (2002) [Hal].
A Monte Carlo method without grid for a fractured porous domain model, Monte Carlo Methods Appl., Fabien Campillo and Antoine Lejay, 8:2, 129-148 (2002) [Hal].
BSDE driven by Dirichlet Process and Semi-linear Parabolic PDE. Application to Homogenization, Stochastic Proces. Appl., Antoine Lejay, 97:1, 1-39 (2002) [Hal].

2001

On the decomposition of excursions measures of processes whose generators have diffusion coefficients discontinuous at one point, Markov Process. Related Fields, Antoine Lejay, 8:1, 117-126 (2001) [Hal].
A Probabilistic Approach of the Homogenization of Divergence-Form Operators in Periodic Media, Asymptot. Anal., Antoine Lejay, 28:2, 151-162 (2001) [Hal].
Homogenization of divergence-form operators with lower-order terms in random media, Probab. Theory Related Fields, Antoine Lejay, 120:2, 255-276 (2001) [Hal, Journal].
{Proc} Weak solution of semi-linear PDE, BSDE and homogenization, Monte Carlo Methods Appl. 7:3-4, 265-272 [Monte Carlo 2000] [Hal]
{Proc} A Monte Carlo Method to Compute the exchange coefficient in the double porosity model, Monte Carlo Methods Appl. 7:1-2, 65-72 [Monte Carlo 2000] [Hal]

2000

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

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Last update of this document: 23 August 2010