Link on my HAL page for publications after 2004.

Link on my arXiv page for publications after 2004.
 

List of publications The publications are gathered according to the main research themes and you can see the corresponding  abstracts (Abstract.pdf files) on this page. Notes aux Comptes Rendus announcing results published in forthcoming papers are not included in this list. The  .dvi or .pdf files of the most recent publications can be downloaded from this page, from HAL or from arXiv .
 

I - ERGODIC THEORY

1. Dilatations de certaines contractions de Lp,  C.R. Acad. Paris, Série A t.283 (1976), p. 1041-1043.

2. Un théorème ergodique en moyenne, C.R. Acad. Sc. Paris, Série A t. 283 (1976),p. 1103-1106. 

3. On the existence of sigma-finite invariant measures for Lp-operators, Israel Journal of Mathematics 33 (1979), p. 349-367 (with L. Sucheston).

4. Sur le théorème en moyenne d'Akcoglu-Sucheston, Mathematische Zeitschrift 172 (1980), p. 213-237.

5. On fixed points and multiparameter ergodic theorems in Banach lattices, Canadian Journal of Mathematics 40 (1988), p. 429-458 (with L. Sucheston).

II - PROCESSES INDEXED BY DIRECTED SETS

1. Sur la caractérisation des conditions de Vitali par la convergence essentielle des martingales, C.R. Acad. Sc. Paris, Série A t. 287 (1978), p. 887-890.

2. Characterization of Vitali conditions with overlap in terms of convergence of classes of amarts, Canadian Journal of Mathematics 31 (1979), p. 1033-1046 (with L. Sucheston).

3. La convergence essentielle des martingales bornées dans L1 n'implique pas la condition de Vitali V, C.R. Acad. Sc. Paris, Série A t. 288 (1979), p. 595-598 (with L. Sucheston).

4. Convergence of classes of amarts indexed by directed sets - Characterization in terms of Vitali conditions, Canadian Journal of Mathematics 32 (1980) , p. 86-125 (with L. Sucheston).

5. A characterization of Vitali conditions in termsof maximal inequalities, The Annals of Probability 8 (1980), p. 339-349 (with L. Sucheston).

6. On convergence of L1-bounded martingales indexed by directed sets, Probability and Mathematical Statistics 1 (1980), p. 151-169 (with L. Sucheston).

7. On covering conditions and convergence, Proceedings of the Conference on Measure Theory, Oberwolfach 1979, Lecture Notes in Mathematics 794 (1980), p. 431-454

III - TWO PARAMETER PROCESSES

1. Régularité à gauche des gauche des martingales fortes à plusieurs indices, C.R. Acad. Sc. Paris, Série A t.290 (1980), p. 773-776 (with J.P. Fouque).

2. On regularity of multiparameter amarts and martingales, Zeitschrift für Wahrscheinlichkeitstheorie verwandte Gebiete 56 (1981), p. 21-45 (with L. Sucheston).

3. On compactness and optimality of stopping times, Proceedings of the Conference on Martingale Theory in Harmonic Analysis and Banach Spaces, Lecture Notes in Mathematics 939 (1981), p. 36-61 (with G.A Edgar and L. Sucheston).

4. Convergence and regularity of strong submartingales, Processus Aléatoires à deux Indices, Proceedings du Colloque E.N.S.T.- C.N.E.T. Paris 1980, Lecture Notes in Mathematics 863 (1981), p. 50-58.

5. On convergence and regularity of (Delta 1) submartingales, Annales de l'Institut Henri Poincaré 19 (1983), p. 25-42.

6. Demi-convergence of processes indexed by two indices, Annales de l'Institut Henri Poincaré 19 (1983), p. 175-187 (with L. Sucheston).

IV - OPTIMAL STOPPING AND CONTROL

1. On randomized tactics and optimal stopping in the plane, The Annals of Probability 13 (1985), p. 946-965.

2. Points, lignes et systèmes d'arrêt flous et problème d'arrêt optimal, Séminairede Probabilités XX, Lecture Notes in Mathematics 1204 (1986), p. 81-94 (with G. Mazziotto). 

3. Stochastic control of two-parameter processes; application to the two-armed bandit problem, Stochastics 22 (1987), p. 251-288 (with G. Mazziotto).

4. A probabilistic approach of the reduite, Probability and Mathematical Statistics 13 (1992), p. 97-121, (with N. El Karoui and J.P. Lepeltier). File.pdf

V - STOCHASTIC CALCULUS OF VARIATIONS AND INFINITE DIMENSIONAL ANALYSIS

1. Integration by parts and time reversal for diffusion processes, The Annals of Probability 17 (1989),p. 208-238 (with D. Nualart and M. Sanz-Solé).

2. Time reversal for infinite dimensional diffusions, Probability Theory and Related Fields 82 (1989), p. 315-347 (with D. Nualart and M. Sanz-Solé).

3. Absolute Continuity of the law of an infinite-dimensional Wiener functional with respect to the Wiener probability, Probability Theory and Related Fields 85 (1990), p. 403-411 (with G. Mazziotto). File.pdf

4. An introduction to the stochastic calculus of variations and to the anticipative calculus, publication de l'Université de Torun (1990).

5. On the continuity of Ornstein-Uhlenbeck processes in infinite dimension, Probability Theory and Related fields 92 (1992), p. 529-547 (with W. Smolenski). File.pdf

6. Small perturbations of Gaussian regressors, Statistics and Probability Letters 24 (1995), p. 21-31 (with W. Smolenski). File.pdf

7. Points of positive density for the solution to a hyperbolic SPDE, Potential Analysis 7 (1997), p. 623-659 (with M. Sanz-Solé).  File.pdf

8. Approximation of rough paths of fractional Brownian motion, Random Fields and Applications V Centro Stefano Franscini, Ascona, May 2005 Series: Progress in Probability, Vol. 59, p. 275-304 (2008), (with Marta Sanz-Solé) File.pdf

VI - LARGE DEVIATIONS

1. Small perturbations for quasilinear anticipating stochastic differential equations, International Series of Numerical Mathematics Birkhaüser Verlag Basel Vol. 102 (1991), p. 149-157 (with D. Nualart and M. Sanz-Solé).

2. Composition of large deviation principles and applications, Stochastic Analysis : Liber Amicorum for Moshe Zakai, Academic Press 1991, p. 383-396 (with D.  Nualart and M. Sanz-Solé). File.pdf

3. Large deviations for a class of anticipating stochastic differential equations, The Annals of Probability 20 (1992), p. 1902-1931, (with D. Nualart and M. Sanz-Solé). File.dvi

4. Varadhan estimates for the density of the solution to a parabolic stochastic partial differential equation, Stochastic Processes and their Applications, Proceedings of the fifth Gregynog Symposium, World Scientific (1996), p. 330-342 (with M. Sanz-Solé). File.pdf

5. Uniform large deviations for parabolic SPDEs and applications, Stochastic Processes and their Applications 72 (1997), p. 161-186 (with F. Chenal) File.pdf.

6. Large Deviations for Stochastic flows and anticipating SDEs in Besov-Orlicz spaces, Stochastics and Stochastic Reports 63 (1998), p. 267-302, (with M. Mellouk). File.pdf

7. Law of iterated logarithm for parabolic SPDEs, Seminar on Stochastic Analysis, Random Fields and Applications (Ascona 1996), p. 101-123, Progr. Probab. 45, Birkhäuser, Basel, 1999 (avec F. Chenal).

8. Large deviations for rough paths of the fractional Brownian motion, Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 42 (2006), n°2, p. 245-271 (avec M. Sanz-Solé).

9. Large deviations for the Boussinesq equation under random influences, Stochastic Processes and their Applications 119-6, p. 2052-2081, (2009), (with J. Duan). doi:10.1016/j.spa.2008.10.004 See also the author's file File.pdf

10. Stochastic 2D hydrodynamical type systems : well-posedeness and large deviations, Applied Mathematics and Optimization. 61 (2010), n°3, p.379-420., doi 10.1007/s00245-009-9091-z (with I. Chueshov). See also the author's file File.pdf

11. Large deviation principle and inviscid shell models, Electronic Journal of Probability Vol. 14 Paper 89 (2009), p. 2581-2579 (with H. Bessaih) Link EJP

12. LDP and the zero viscosity limit for the 2D stochastic NSE with a free boundary, SIAM Journal on Mathematical Analysis, 2012 , Vol. 44, No. 3, pp. 1861-1893 (with H. Bessaih)

VII - SUPPORT THEOREMS

1. Support theorems for a class of anticipating stochastic differential equations, Stochastics and Stochastics Reports 39 (1992), p. 1-24 (with D. Nualart). File.dvi

2. Un théorème de support pour une équation aux dérivées partielles stochastiques hyperbolique, C. R. Acad. Sc. Paris, Série I, t. 315 (1992), p. 615-618 (with M. Sanz-Solé).

3. On the support of a Skorohod anticipating stochastic differential equation, Barcelona Seminar on Stochastic Analysis, Progress in Probability Vol. 32, p. 103-131, Birkhaüser Verlag, Basel (1993) (with M. Sanz-Solé). File.pdf

4. The support of the solution to a hyperbolic SPDE, Probability Theory and Related Fields 98 (1994), p. 361-387 (with M. Sanz-Solé) File.dvi

5. A simple proof of the support theorem for diffusion processes, Séminaire de Probabilités XXVIII (1994), Lecture Notes in Mathematics 1583, p. 36-48 (with M. Sanz-Solé). File.dvi

6. Approximation and support theorem in Hölder norm for parabolic stochastic partial differential equations, The Annals of Probability 23 (1995), p. 178-222 (with V. Bally and M. Sanz-Solé). File.dvi

7. Approximation and support theorem for a two-space dimensional wave equation, Bernoulli 6 (5) (2000), p. 887-915 (with M. Sanz-Solé). File.pdf 

8. A support theorem for a generalized Burgers equation, Potential Analysis 15 (2001), p. 361-408 (with C. Cardon-Weber). File.pdf

9. Stochastic 2D hydrodynamical systems : Wong-Zakai approximation and Support theorem, Stochastic Analysis and Applications 29 (2011), 4, p. 570-611. (with I. Chueshov).

VIII - EXISTENCE, REGULARITY OF SOLUTIONS TO LINEAR and NON LINEAR STOCHASTIC PDEs

1. A stochastic wave equation in two space dimension: smoothness of the law, The Annals of Probability 27 (1999), p. 803-844 (with M. Sanz-Solé). File.pdf

2. On a stochastic wave equation in two space dimension: regularity of the solution and its density, Stochastic Processes and their Applications 86 (2000), p. 141-162 (with P.L. Morien). File.pdf

3. On a non linear stochastic wave equation in the plane: existence and uniqueness of the solution, The Annals of Applied Probability  11 (2001), p. 922-951 (with P.-L. Morien). File.pdf

4. On strongly Petrovskii's parabolic SPDEs in arbitrary dimension and application to the stochastic Cahn-Hilliard equation,   Journal of Theoretical Probability   17-1 (2004), p. 1-49 (with C. Cardon-Weber). File.pdf

Vous pouvez voir le résumé sur le site  Kluwer

5. On the stochastic Strichartz estimates and the stochastic nonlinear Schrödinger equation on a compact riemannian manifold, Potential Analysis 30-1 (2009), p. 29-64 DOI 10.1007/s11118-013-9369-2 (with Z. Brzezniak).

6. Existence and regularity of solutions for a stochastic Cahn-Hilliard / Allen-Cahn equation with unbounded noise coefficient, , J. of Differential Equations 260-3 (2016), p. 2383-2417 DOI 10.1016/jde2015.10.004 (with D. Antonopoulo and G. Karali).

7. On stochastic modified 3D Navier Stokes with anisotropic viscosity, J. of Mathematical Analysis and Applications, 462-1 (2018), p. 915-956, DOI 10.1016/j.jmaa.2017.12.053 (with H. Bessaih).

8. Generalized KdV equation subject to a stochastic perturbation, Discrete and Continuous Dynamical Systems, Series B , 23-3 (2018), p. 1177-1198 DOI10.3934/dcdsb.2018147 (with S. Roudenko).

9. Global solutions to stochastic wave equations with superlinear coefficients, Stochastic Processes and their Applications, 139 (2021), p. 175-211, DOI (with M. Sanz-Solé).

IX - DISCRETIZATION OF SOLUTIONS TO STOCHASTIC PDEs

1.  On implicit and explicit discretization schemes for parabolic SPDEs in any dimension,  Stochastic Processes and their Applications  115-7 (2005), p. 1073-1106 (with P.L. Morien). File.pdf

2. On discretization schemes for stochastic evolution equations,  Potential Analysis  Vol. 23 (2005),  p. 99-134 (with I. Gyöngy). File.pdf

3. Rate of Convergence of Implicit Approximations for stochastic evolution equations, Stochastic Differential Equations: Theory and Applications A volume in Honor of Professor Boris L. Rosovskii, Interdisciplinary Mathematical Sciences, Vol 2  World Scientific (2007), p. 281-310  (with I. Gyöngy) See also the author's file File.pdf

4. Rate of Convergence of Space Time Approximations for stochastic evolution equations, Potential Analysis 30-1 (2009), p. 29-64 DOI 10.1007/s11118-008-9105-5 (with I. Gyöngy) See also the author's file  File.pdf  

5. On the splitting method for some complex-valued quasilinear evolution equations, 9th Workshop on Stochastic Analysis and Related Topics (in Honour of Ali Süleyman Üstünel, Paris June 2010), Proceedings in Mathematics and Statistics, Vol 22, Springer Verlag, p. 57-90 (2012), (with Z. Brzezniak).

6. Splitting up method for the 2D stochastic Navier-Stokes equations, Stochastic Partial Differential Equations, Analysis and Computations 2-4 (2014), p. 433-470 DOI 10.1007/s40072-014-0041-7 (with H. Bessaih and Z. Brzezniak)

7. Strong L^2 convergence of time numerical schemes for the stochastic 2D Navier-Stokes equation, IMA Journal of Numerical Analysis, 39-4 (2019), p. 2135-2167 DOI 10.1093/imanum/dry059 , (with H. Bessaih).

8. Space-time Euler discretization schemes for the stochastic 2D Navier-Stokes equations, Stochastic Partial Differential Equations, Analysis and Computations 10-4 (2022), p. 1515-1558 DOI , (with H. Bessaih).

9. Behavior of solutions to the 1D focusing stochastic L^2-critical and supercritical nonlinear Schrödinger equation with space-time white noise, IMA Journal of Applied Mathematics , 86-6 (2021) DOI (with S. Roudenko and K. Yang).

10. Behavior of solutions to the 1D focusing stochastic nonlinear Schrödinger equation with spatially correlated noise, Stochastic Partial Differential Equations, Analysis and Computations , 9-4 (2021), p. 1031-1080 DOI (with A. Rodriguez, S. Roudenko and K. Yang).

11. Strong rates of convergence of space-time discretization schemes for the 2D Navier-Stokes equations with additive noise, Stochastic and Dynamics, 22-2 (2022), paper 224005 DOI (with H. Bessaih),

12. Strong L^2 convergence of time Euler schemes for 3D Brinkman-Forchheimer-Navier-Stokes equations, Stochastic Partial Differential Equations: Analysis and Computations 10-3 (2022), p. 1005-1049 DOI (with H. Hessaih).

13. Speed of convergence of time Euler schemes for a stochastic 2D Boussinesq model, Mathematics (Special issue "Computational Methods in Nonlinear Analysis" 10, paper 4246 (2022) link (with H. Bessaih).