Cette page est en lecture seule. Vous pouvez afficher le texte source, mais ne pourrez pas le modifier. Contactez votre administrateur si vous pensez qu'il s'agit d'une erreur. ===== Research Themes ====== ====== Publications ====== ===== Books ===== [L7] // Stochastic Partial Differential Equations. An Introduction.// SpringerBriefs in Mathematics, Springer 2021. [L6] {{ :pm_root.pdf |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. A Chinese translation has appeared in 2019. [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 ===== [166] {{ :en:ak-ep_nomouv_bded_arxiv.pdf |Spatial SIR epidemic model with varying infectivity without movement of individuals}}, with A. Kanga, //Pure and Applied Funct. Analysis//, to appear. [165] {{ :en:crisanpardoux_arxiv.pdf |Uniqueness of the solution of the filtering equations in spaces of measures}}, with D. Crisan, arXiv:2411.11125. [164] {{ :en:spde_pangpardoux_arxiv.pdf |SPDE for stochastic SIR epidemic models with infection-age dependent infectivity}}, with G. Pang, arXiv2410.17200. [163] {{ :en:clt_dim1_revised.pdf |A SIR epidemic model on a refining spatial grid II-central limit theorem}}, with T. Gallouët and T. Yeo, //Stoch. PDE : Anal. Comp.// **13**, 1, pp. 146-179, 2025. [162] {{ :en:mathematics-12-02826.pdf |Epidemic models with varying infectivity on a refining spatial grid. I. The SI model}}, with A. Mougabe-Peurkor and T. Yeo, //Mathematics// **12**, 2024. [161] {{ :fr:clt_vuong.pdf |Central limit theorem for a spatial stochastic epidemic model with mean field interaction}}, with M. Hauray and Y. Vuong, arXiv:2212.02149 . [160] {{ :fr:2304.05211.pdf |Spatially dense stochastic epidemic models with infection-age dependent infectivity}}, with G. Pang, arXiv:2304.05211. [159] {{ :en:article_temps_d_extinction_ruma.pdf |Extinction time of an epidemic with infection age dependent infectivity}}, with A. Mougabe-Peurkor, I. Drame and M. N'zi, //Revista de la Union Matematica Argentina// **67**, pp. 417-443, 2024. [158] {{ :en:pafav9n3p863-published.pdf |PDE model for multi-patch epidemic models with migration and infection-age dependent infectivity}}, with G. Pang, //Pure and Applied Funct. Analysis// **9**, 3, pp.863-897, 2024. [157] {{ :en:epidemic_vvis-revised-update9.pdf |Stochastic epidemic models with varying infectivity and waning immunity}}, with R. Forien, G. Pang and A.B. Zotsa Ngoufack, //Annals of Applied Probability//, to appear. [156] {{ :en:puqr2022019-forien.pdf |Multi-patch multi-group epidemic model with varying infectivity}}, with R. Forien and G. Pang, // Probab. Uncertain. Quant. Risk// **7**, 4, pp. 333-364, 2022. [155] {{ :en:corrected_poc_spatial_epidemic_model.pdf |Conditional propagation of chaos in a spatial stochastic epidemic model with common noise}}, with M.Hauray and Y.V. Vuong, //Stochastic and Partial Differential Equations// **10**, 3, pp. 1180-1210, 2022 [154] {{ :en:auretmauro.pdf |Metastability between the clicks of the Müller ratchet}}, with M. Mariani and A. Velleret, // Probab. Theory Related Fields //, to appear. [153] {{ :en:survey_forien-pang-pardoux2021.pdf |Recent advances in epidemic modeling : non Markov stochastic models and their scaling limits}}, with R. Forien and G. Pang, //Graduate J. Math.// **7**, 19--75, 2022. [152] {{ :en:fllnandpdes_amo_published.pdf |Functional law of large numbers and PDEs for epidemic models with infection-age dependent infectivity}}, with G. Pang, //Applied Math. & Optimization// **87**, 2023. [151] {{ :en:fclt-varying_infectivity_revision5.pdf |Functional central limit theorems for epidemic models with varying infectivity}}, with G. Pang, //Stochastics// **95**, 819--866, 2023. [150] {{ :fr:bep.pdf |A Spatial Stochastic Epidemic Model: Law of Large Numbers and Central Limit Theorem}}, with S. Bowong and A. Emakoua, //Stoch. PDE : Anal. Comp.// **11**, pp. 31-105, 2023. [149] {{ :en:rsos.202327.pdf |Estimating the state of the Covid-19 epidemic in France using a non-Markovian model}}, with R. Forien and G. Pang, // R. Soc. Open Sci.// **8**:202327, 2021. [148] {{ :en:varying_infectivity-siam-final.pdf |Epidemic models with varying infectivity}}, with R. Forien and G. Pang, //SIAM J. Applied Math.//, **81**, pp. 1893-1930, 2021. [147] {{ :en:multipatch_arxiv_may21.pdf |Multi-patch epidemic models with general infectious periods}}, with G. Pang, //ESAIM P & S// **27**, pp. 345-401, 2023. [146] {{ :en:funct_limit_theorem_gp-ep_arxiv.pdf |Functional limit theorems for non-Markovian epidemic models}}, with G. Pang, //Annals of Applied Probability// **32** pp. 1615-1665, 2022. [145] {{ :drame-pardoux_tims_final.pdf |Approximation of the height process of a continuous state branching process with interaction}}, with I. Dramé, //Theor. Probability and Math. Statist.// **103**, pp. 3-39, 2020. [144] {{ :en:hairer-pardoux2021_article_fluctuationsaroundahomogenised.pdf |Fluctuations around a homogenized semilinear random PDE}}, with M. Hairer, //Archive for Rational Mechanics and Analysis// ** 239**, pp. 151-217, 2021. [143] {{ :en:householdsde_paper.pdf |Household epidemic models and McKean-Vlasov Poisson driven SDEs}}, with R. Forien, //Annals of Applied Probability// **32**, pp. 1210-1233, 2022. [142] {{ :en:ejp_moddev_published.pdf |Moderate Deviations and Extinction of an Epidemic}}, //Electron. J. Probab.// **25**, paper no. 25, 1-27, 2020. [141] {{ :en:epardoux_cimom18_revised.pdf |Deviations from the law of large numbers, and extinction of an endemic disease}}, in //Mathematical modeling of random and deterministic phenomena//, Manou--Abi, S.M., Dabo--Niang, S., Salone, J.J. eds., pp. 3--30, ISTE and Wiley, 2020. [140] {{ :en:li2022_article_theheightprocessofacontinuous-.pdf |The height process of a continuous state branching process with interaction}}, with Z. Li and A. Wakolbinger, // J Theor Probab // **35**, pp. 142--185, 2022. [139] {{ ::aihp1807-002ra0.pdf |Extinction time and the total mass of the continuous state branching processes with competition}}, with Vi Le, //Stochastics// **92**, pp. 852-875, 2020. [138] {{ :en:nzi2021_article_asirmodelonarefiningspatialgri.pdf |A SIR model on a refining spatial grid I - Law of Large Numbers}}, with Modeste N'zi and Ténan Yeo, //Applied Math. & Optimization// **83**, pp. 1153-1189, 2021. [137] {{ :en:rootparti.pdf |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. **2255**, pp. 1--120, Springer 2019. [136] {{ :articleesaim-ps_2020.pdf |Large deviation of the exit measure through a characteristic boundary for a Poisson driven SDE}}, with Brice Samegni-Kepgnou, //ESAIM P & S// **24**, pp. 148-185, 2020. [135] {{ :id-ep_ecpparu.pdf |Approximation of a generalized CSBP with interaction}}, with Ibrahima Dramé, //Electron. Commun. Probab.//, **23** , 73, 1-14, 2018. [134] {{ :ldp_reflected_april18.pdf |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] {{ :sjl_revised-2018.pdf |Small jumps asymptotic of the moving optimum Poissonian SDE}}, with Elma Nassar, //Stochastic Processes and Applications// **129**, pp. 2320-2340, 2019. [132] {{ :kopp2018_jmb.pdf |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_2016.pdf |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] {{ :nonlinearfilteringdegennoise.pdf |Nonlinear filtering with degenerate noise}}, with David Jaurès Fotsa-Mbogne, //Electron. Commun. Probab.// **22** , Paper No. 44, 14 pp., 2017 [129] {{ :sam-pard-jap.pdf |Large Deviation principle for Epidemic Models}}, with Brice Samegni-Kepgnou, //Journal Appli. Prob.//**54**, 905-920, 2017. [128] {{ :continuity_fk_janvier2016.pdf |Continuity of the Feynman-Kac formula for a generalized parabolic equation}}, with A. Rascanu, //Stochastics//, **89** ,726-752, 2017. [127] {{ :articlejap_revised2.pdf |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] {{ :khalifa_et_al.pdf |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] {{ :dramepardouxsow.pdf |Non-binary branching process and non-Markovian exploration process}}, with I. Dramé and A.B. Sow, //ESAIM P & S// , **21**, 1-33, 2017 [124] {{ :bahlalielouaflinpardouxspa17.pdf |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] {{ :bmpr.pdf |Stochastic variational inequalities on non-convex domains}}, with R. Buckdahn, L. Maticiuc and A. Rascanu, //J. Differential Equations//, **259**, 7332-7374, 2015. [122] {{ :dpp.pdf |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] {{ :07-7206_hairer.pdf |A Wong-Zakai theorem for stochastic PDEs}}, with M. Hairer, //J. Math. Soc. Japan// **67**, 1-54, 2015. [120] {{ :ep-aw-15.pdf |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] {{ :le_pardouxesaim-ps.pdf |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] {{ :aihp621.pdf |Branching processes with competition and generalized Ray Knight Theorem}}, with M. Ba, //Annales de l'Institut Henri Poincaré - Probabilités et Statistiques// **51**, 1290-1313, 2015. [117] {{ :bbah_epardoux.pdf |Lambda-lookdown model with selection}}, with B. Bah, //Stochastic Processes and Applications//, **125**, 1089-1126, 2015. [116] {{ :proc144807.pdf |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] {{ :invmeasureselectiondec2013-final.pdf |Invariant measure selection by noise. An example}}, with J. Mattingly, //Discrete Contin. Dyn. Syst.// **34**, no. 10, 4223-4257, 2014. 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[110] {{ :festschriftdn.pdf |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] {{ :bb_ep_bs_springer.pdf |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] {{ :aop650.pdf |Homogenization of a singular random on dimensional parabolic PDE with time varying coefficients}}, with Piatnitski, Andrey, //Annals of Probab.// **40**, pp. 1316-1356, 2012. 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