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Research Themes

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Publications

Books

[L6] Probabilistic models of population evolution. Scaling limits and interactions. Springer, 2016.

[L5] Stochastic Differential Equations, Backward SDEs, Partial Differential Equations (with A. Rascanu), Stochastic Modelling and Applied Probability 69, Springer 2014.

[L4] Markov processes and applications. Algorithms, networks, genome and finance. Translated and revised from the 2007 French edition. Wiley Series in Probability and Statistics. John Wiley & Sons, Ltd., Chichester; Dunod, Paris, 2008.

[L3] Processus de Markov et applications. Algorithmes, réseaux, génome et finance, Dunod, Paris, 2007.

[L2] Méthodes de Monte-Carlo pour les équations de transport et de diffusion (with Lapeyre, Bernard; Sentis, Rémi), Mathématiques & Applications (Berlin) [Mathematics & Applications] ,29. Springer-Verlag, Berlin, 1998. x+176 pp. ISBN: 3-540-63393-6 Engl. translation by Alan Craig and Fionn Craig: Introduction to Monte-Carlo methods for transport and diffusion equations. Oxford Texts in Applied and Engineering Mathematics, 6, Oxford University Press, Oxford, 2003. x+163 pp. ISBN: 0-19-852593-1

[L1] Méthodes Probabilistes pour les Equations de la Physique (with M. Cessenat, G. Ledanois, P.L. Lions and R. Sentis, R. Dautray ed.), Eyrolles, 1989.

Articles

[144] Approximation of the height process of a continuous state branching process with interaction (with I. Dramé), submitted.

[143] Fluctuations around a homogenized semilinear random PDE (with M. Hairer), submitted.

[142] Household epidemic models and McKean-Vlasov Poisson driven SDEs (with R. Forien), submitted.

[141] Moderate Deviations and Extinction of an Epidemic, submitted.

[140] The height process of a continuous state branching process with interaction (with Z. Li and A. Wakolbinger), submitted.

[139] Extinction time and the total mass of the continuous state branching processes with competition (with Vi Le), Stochastics, to appear.

[138] A SIR model on a refining spatial grid I - Law of Large Numbers (with Modeste N'zi and Ténan Yeo), Applied Math. & Optimization, to appear.

[137] Stochastic epidemics in a homogeneous community (with Tom Britton), Part I of Stochastic Epidemic Models with Inference, T. Britton and E. Pardoux eds., Lecture notes in Math., Springer 2019.

[136] Large deviation of the exit measure through a characteristic boundary for a Poisson driven SDE (with Brice Samegni-Kepgnou), submitted.

[135] Approximation of a generalized CSBP with interaction (with Ibrahima Dramé), Electron. Commun. Probab., 23 , 73, 1-14, 2018.

[134] Large Deviation Principle for Reflected Poisson driven SDEs in Epidemic Models (with Brice Samegni-Kepgnou), Stochastic Analysis and Applications 37, pp. 836-864, 2019.

[133] Small jumps asymptotic of the moving optimum Poissonian SDE (with Elma Nassar), Stochastic Processes and Applications 129, pp. 2320-2340, 2019.

[132] Phenotypic lag and population extinction in the moving-optimum model: insights from a small-jumps limit (with Michael Kopp and Elma Nassar), J. Math. Biol., 77, pp. 1431-1458, 2018.

[131] Large deviations for infectious diseases models, (with Peter Kratz), Séminaire de Probabilités XLIX, C. Donati-Martin, A. Lejay, A. Rouault eds., Lecture Notes in Math. 2215, pp. 221-327, 2018.

[130] Nonlinear filtering with degenerate noise (with David Jaurès Fotsa-Mbogne), Electron. Commun. Probab. 22 , Paper No. 44, 14 pp., 2017

[129] Large Deviation principle for Epidemic Models, (with Brice Samegni-Kepgnou), Journal Appli. Prob.54, 905-920, 2017.

[128] Continuity of the Feynman-Kac formula for a generalized parabolic equation, (with A. Rascanu), Stochastics, 89 ,726-752, 2017.

[127] On the long time behavior of the solution of an SDE driven by a Poisson Point Process, (with E. Nassar), Adv. in Appl. Probab. 49, 344-367, 2017.

[126] TMEM187-IRAK1 Polymorphisms Associated with Rheumatoid Arthritis Susceptibility in Tunisian and French Female Populations: Influence of Geographic Origin, (with O. Khalifa, N. Balandrauid, N. Lambert, I. Auger, J. Roudier, A. Sénéchal, D. Geneviêve, C. Picard, G. Lefranc, I. Touitou, B. M'Madi Mrenda, C. Benedito, A.-L. Gagez, Y.-M. Pers, C. Jorgensen, T. Mahjoub et F. Apparailly)), Journal of Immunology Research, 2017, Article ID 4915950, 12 pages, 2017.

[125] Non-binary branching process and non-Markovian exploration process, (with I. Dramé and A.B. Sow), ESAIM P & S , 21, 1-33, 2017

[124] Averaging for SDE-BSDE with null recurrent fast component Application to homogenization in a non periodic media (with Khaled Bahlali and A. Elouaflin), Stochastic Processes and Applications, 127, 1321-1353, 2017.

[123] Stochastic variational inequalities on non-convex domains (with R. Buckdahn, L. Maticiuc and A. Rascanu), J. Differential Equations, 259, 7332-7374, 2015.

[122] A mixing tree-valued process arising under neutral evolution with recombination, with A. Depperschmidt, P. Pfaffelhuber, Electron. J. Probab., 20 no. 94, 1-22, 2015.

[121] A Wong-Zakai theorem for stochastic PDEs, with M. Hairer, J. Math. Soc. Japan 67, 1-54, 2015.

[120] A path-valued Markov process indexed by the ancestral mass, with A. Wakolbinger, ALEA Lat. Am. J. Probab. Math. Stat., 12, 193-212, 2015.

[119] Height and the total mass of the forest of genealogical trees of a large population with general competition, with Vi Le, ESAIM : Probability and Statistics, 19, 172-193, 2015.

[118] Branching processes with competition and generalized Ray Knight Theorem, avec M. Ba, Annales de l'Institut Henri Poincaré - Probabilités et Statistiques 51, 1290-1313, 2015.

[117] Lambda-lookdown model with selection, with B. Bah, Stochastic Processes and Applications, 125, 1089-1126, 2015.

[116] Numerical methods in the context of compartmental models in epidemiology, with P. Kratz and B. Samegni Kepnou, ESAIM : Proceedings and Surveys 48, 169-189, 2014.

[115] Invariant measure selection by noise. An example, with J. Mattingly, Discrete Contin. Dyn. Syst. 34, no. 10, 4223-4257, 2014.

[114] HLA-DRB1 genotypes and the risk of developing anti citrullinated protein antibody (ACPA) positive rheumatoid arthritis (with Nathalie Balandraud, Christophe Picard, Denis Reviron, Cyril Landais, Eric Toussirot, Nathalie Lambert, Emmanuel Telle, Caroline Charpin, Daniel Wendling, Isabelle Auger, Jean Roudier), PLOS ONE 8, N 5, May 201

[113] Random homogenisation of a highly oscillatory singular potential, with M. Hairer and A. Piatnitski, Stoch. PDE : Anal. Comp. 1, 571-605, 2013.

[112] Muller's ratchet clicks in finite time. (with Julien Audiffren), Stochastic Processes and Applications 123, 2370 - 2397, 2013. .

[111] Trees under attack: a Ray-Knight representation of Feller's branching diffusion with logistic growth (with V. Le, A. Wakolbinger), Probab. Theory Relat. Fields 155, 583-619, 2013.

[110] The effect of competition on the height and length of the forest of genealogical trees of a large population. (with Mamadou Ba), in Malliavin Calculus and Related Topics, a Festschrift in Honor of David Nualart, F. Viens, J. Feng, Y. Hu, E. Nualart Eds., Springer Proceedings in Mathematics and Statistics 34, 445-467, 2012.

[109] A look-down model with selection. (with B. Bah, A. B. Sow), in Stochastic Analysis and Related Topics, Laurent Decreusefond et Jamal Najim Ed, Springer Proceedings in Mathematics and Statistics Vol 22, 1-28, 2012.

[108] Homogenization of a singular random on dimensional parabolic PDE with time varying coefficients (with Piatnitski, Andrey), Annals of Probab. 40, pp. 1316-1356, 2012.

[107] Binary trees, exploration processes, and an extended Ray-Knight Theorem (with Ba, Mamadou et Sow, Ahmadou, Bamba), Journal of Applied Probability 49, 210-225, 2012.

[106] From Brownian motion with a local time drift to Feller's branching diffusion with logistic growth (with A. Wakolbinger), Electronic. Comm. Probab. 16, 720-731, 2011.

[105] Homogenization of a periodic degenerate semilinear elliptic PDE (avec A. B. Sow), Stochastics and Dynamics 11, 475-493, 2011.

[104] Compound Poisson approximation and testing for gene clusters with multigene families (with S. Grusea, O. Chabrol, P. Pontarotti), J. Comput. Biol. 18 , 579-594, 2011.

[103] From exploration paths to mass excursions - variations on a theme of Ray and Knight.(with Wakolbinger, Anton), in Surveys in Stochastic Processes, Proc. 33rd SPA Conf. Berlin, 2009, J. Blath, P. Imkeller, S. Roelly eds. EMS Series of Congress reports, 87-106, 2011.

[102] Survival of a single mutant in one dimension (with Andjel, Enrique; Miller, Judith), Electronic J. Probab 15, 2010.

[101] A weak convergence theorem for particle motion in a stochastic field (with Elskens, Yves), Annals of Applied Probab., 20, 2022-2039, 2010.

[100] Evolution of the ancestral recombination graph along the genome in case of a selective sweep. (with Léocard, Stéphanie) J. Math. Biology 61, 819-841, 2010.

[99] Viscosity solutions for systems of parabolic variational inequalities (with Maticiuc, Luciani; Rascanu, Aurel; Zalinescu, Adrian), Bernoulli 16, 258-273, 2010.

[98] On the height and length of the ancestral recombination graph (with Salamat, Majid), J. Appl. Prob. 46, 669-689, 2009.

[97] A probabilistic formula for a Poisson equation with Neumann boundary conditions (with Benchérif-Madani, Abdellatif), Stoch. Anal. Appl. 27, 739-746, 2009.

[96] Homogenization of periodic semilinear parabolic degenerate PDES (avec A. B. Sow, R. Rhodes), Ann. I. H. Poincaré - AN 26,979-998, 2009.

[95] Homogenization of semilinear PDEs with discontinuous averaged coefficients. (with K. Bahlali, A. Elouaflin), Electronic J. of Probability 14, 477-499, 2009.

[94] Homogenization of periodic linear degenerate PDEs. (with M. Hairer), J. Funct. Anal. 255, No. 9, 2462-2487, 2008.

[93] Homogenization of a singular random one-dimensional PDE (with Iftimie, Bogdan; Piatnitski, Andrey), Ann. Inst. Henri Poincaré Probab. Stat. 44, no. 3, 519-543, 2008.

[92] Homogenization of a semilinear parabolic PDE with locally periodic coefficients: a probabilistic approach (with Benchérif-Madani, Abdellatif), ESAIM Probab. Stat. 11, 385-411, 2007.

[91] Homogenization of periodic semilinear hypoelliptic PDEs (with Diédhiou, Alassane), Ann. Fac. Sci. Toulouse Math. 16, no. 2, 253-283, 2007.

[90] Malliavin calculus for the stochastic 2D Navier-Stokes equation (with Mattingly, Jonathan C.), Comm. Pure Appl. Math. 59 (2006), 1742-1790, 2006.

[89] Homogenization of a singular random one dimensional PDE (with Piatnitski, Andrey), in Multi scale problems and asymptotic analysis, 291-303, GAKUTO, Internat. Ser. Math. Sci. Appl. 24, Gakkotosho, Tokyo, 2006.

[88] Singular homogenization with stationary in time and periodic in space coefficients (with Diop, M. A.; Iftimie, B.; Piatnitski, A. L.), J. Funct. Anal. 231, no. 1, 1-46, 2006.

[87] On the Poisson equation and diffusion approximation III (with Veretennikov, A. Yu.), Ann. Probab. 33, no. 3, 1111-1133, 2005.

[86] Homogenization of a diffusion with locally periodic coefficients (with Benchérif-Madani, Abdellatif), in Séminaire de Probabilités XXXVIII, 363-392, Lecture Notes in Math. 1857, Springer, Berlin, 2005.

[85] Backward stochastic differential equations associated to a symmetric Markov process (with Bally, V.; Stoica, L.), Potential Anal., 22, no. 1, 17-60, 2005.

[84] Quenched large deviations for one dimensional nonlinear filtering (with Zeitouni, Ofer), SIAM J. Control Optim. 43, no. 4, 1272-1297, 2004/05.

[83] Malliavin calculus for highly degenerate 2D stochastic Navier-Stokes equations (with Hairer, Martin; Mattingly, Jonathan C.), C. R. Math. Acad. Sci. Paris 339, no. 11, 793-796, 2004.

[82] Probabilistic interpretation of a system of quasilinear parabolic PDEs (with Sow, A. B.), Stochastics & Stoch. Rep. **7