Topics of Research:

Research articles:

Polynomial convergence rates for Markov kernels under nested modulated drift conditions (with J. Ledoux). Preprint (2023) Computable bounds for solutions to Poisson's equation and perturbation of Markov kernels (with J. Ledoux). Preprint (2023), accepted for publication in Bernoulli. Specific properties of the ODE’s flow in dimension two versus dimension three (with M. Briane). J Dyn Diff Equat 36, 421–461 (2024). Rate of convergence of Nummelin-type representation of the invariant distribution of a Markov chain via the residual kernel (with J. Ledoux). Preprint (2023). Electronic Communications in Probability 2023, Vol. 28, paper no. 58, 1-13. Fine asymptotic expansion of the ODE's flow (with M. Briane). Journal of Differential Equations, 2023, 373, pp.327 - 358. Explicit bounds for spectral theory of geometrically ergodic Markov kernels and applications (with J. Ledoux). Bernoulli 30(1), 2024, 581–609 Robustness of iterated function systems of Lipschitz maps (with J. Ledoux). Journal of Applied Probability 60, 921-944 (2023). Asymptotics of ODE’s flow on the torus through a singleton condition and a perturbation result. Applications. (with M. Briane). Discrete and Continuous Dynamical Systems, Vol. 42, No. 7, July 2022, pp. 3431-3463. A picture of the ODE's flow in the torus: from everywhere or almost-everywhere asymptotics to homogenization of transport equations, 2021 (with M. Briane). Journal of Differential Equations 304 (2021) 165–190. Asymptotic of products of Markov kernels. Application to deterministic and random forward/backward products (with J. Ledoux). Statist. Probab. Lett. 179 (2021) V-geometrical ergodicity of Markov kernels via finite-rank approximations. (with J. Ledoux). Electronic Communications in Probability 2020, Vol. 25, paper no. 23, 1-12. Complements results related to quasi-compactness are presented in the section "Other documents" below. State-discretization of V -geometrically ergodic Markov chains and convergence to the stationary distribution (with J. Ledoux). Methodol. Comput. Appl. Probab. 22 (2020), no. 3, 905–925. Exponential growth of branching processes in a general context of lifetimes and birthtimes dependence (with S. Louhichi and F. Pène). ESAIM: Probability and Statistics, EDP Sciences, 2019, 23, pp.584-606. Multiplicative ergodicity of Laplace transforms for additive functional of Markov chains (with S. Louhichi and F. Pène). ESAIM: Probability and Statistics, EDP Sciences, 2019, 23, pp.607-637. A computable bound of the essential spectral radius of finite range Metropolis-Hastings kernels (with J. Ledoux). Statistics and Probability Letters, 117 (2016) 72-79. Computable bounds of $\ell^2$-spectral gap for discrete Markov chains with band transition matrices (with J. Ledoux). Journal of Applied Probability, 53, 946-952, 2016. Details and numerical illustrations for Metropolis-Hastings kernels are presented in the section "Other documents" below. Spectral analysis of Markov kernels and application to the convergence rate of discrete random walks (with J. Ledoux). Adv. Appl. Prob. 46, 1036-1058 (2014) Approximating Markov chains and V -geometric ergodicity via weak perturbation theory (with J. Ledoux). Stochastic Processes and their Applications 124 (2014) 613–638 Local limit theorem for densities of the additive component of a finite Markov Additive Process (with J. Ledoux). Statistics and Probability Letters 83 (2013) 2119–2128. Complements related to applications to Markov renewal processes and to local times of a finite jump process are presented in the section "Other documents" below. Geometric rho-mixing property of the interarrival times of a stationary Markovian arrival process (with J. Ledoux). Applied Probability Trust, vol. 50, No. 2, 2013. Regular perturbation of V-geometrically ergodic Markov chains (with D. Ferré et J. Ledoux). Journal of Applied Probability, Vol. 50, No. 1 (March 2013). Multidimensional renewal theory in the non-centered case. Application to strongly ergodic Markov chains (with D. Guibourg). Potential Analysis 38:471–497 (2013). On the Recurrence Set of Planar Markov Random Walks (with F. Pène). J. Theor. Probab. 26:169–197 (2013). Limit theorems for stationary processes with L2-spectral gap (with D. Ferré and J. Ledoux). Annales de l’Institut Henri Poincaré - Probabilités et Statistiques 2012, Vol. 48, No. 2, 396–423. A Berry-Esseen theorem of M-estimators for V-geometrical Markov chains (with J. Ledoux; V. Patilea). Bernoulli 18(2), 2012, 703–734. A renewal theorem for strongly ergodic Markov chains in dimension d ≥3 and in the centered case (with D. Guibourg). Potential Analysis, 34, 385-410 (2011). The Nagaev-Guivarc'h method via the Keller-Liverani perturbation theorem (with F. Pène). Bulletin de la Société Mathématiques de France, 138 (3), 2010, 415-489. Quasi-compactness and mean ergodicity for Markov kernels acting on weighted supremum normed spaces. Ann. Inst. Henri Poincaré Probab. Stat. 44 (2008), no. 6, 1090--1095. Vitesse de convergence dans le théorème limite central pour des chaînes de Markov fortement ergodiques. [Rate of convergence in the central limit theorem for strongly ergodic Markov chains] Ann. Inst. Henri Poincaré Probab. Stat. 44 (2008), no. 2, 280--292. Stable laws and products of positive random matrices (with H. Hennion). J. Theoret. Probab. 21 (2008), no. 4, 966--981. Théorème local pour chaînes de Markov de probabilité de transition quasi-compacte. Applications aux chaînes V-géométriquement ergodiques et aux modèles itératifs. (French) [Local theorem for Markov chains with quasicompact transition probability. Applications to V-geometrically ergodic chains and iterative models] Ann. Inst. H. Poincaré Probab. Statist. 41 (2005), no. 2, 179--196. Central limit theorems for iterated random Lipschitz mappings (with H. Hennion). Ann. Probab. 32 (2004), no. 3A, 1934--1984. Limit theorems for Markov chains and stochastic properties of dynamical systems by quasi-compactness (with H. Hennion). Lecture Notes in Mathematics, 1766. Springer-Verlag, Berlin, 2001. Etude du spectre périphérique de certaines perturbations d'opérateurs quasi-compacts (with H. Hennion). (French) [A study of the peripheral spectrum of certain perturbations of quasicompact operators] C. R. Acad. Sci. Paris Sér. I Math. 328 (1999), no. 5, 419--422. Peripheral spectrum of positive quasi-compact operators on $\cC_0(X)$. Integral Equations Operator Theory 32 (1998), no. 2, 199--215. Pavages auto-affines, opérateurs de transfert et critères de réseau dans $R\sp d$ (with J.-P. Conze, A. Raugi). (French) [Self-affine tilings, transfer operators and criteria for lattices in $R\sp d$] Bol. Soc. Brasil. Mat. (N.S.) 28 (1997), no. 1, 1--42. Transformée en paquets d'ondelettes des signaux stationnaires: comportement asymptotique des densités spectrales (French) [Wavelet packet transform of stationary signals: asymptotic behavior of the spectral densities] Rev. Mat. Iberoamericana 12 (1996), no. 3, 653--667. Construction et régularité des fonctions d'échelle. (French) [Construction and regularity of scaling functions] SIAM J. Math. Anal. 26 (1995), no. 5, 1361--1385. Comportement asymptotique dans l'algorithme de transformée en ondelettes. Lien avec la régularité de l'ondelette (French) [Asymptotic behavior of the wavelet transform algorithm. Connection with the regularity of the wavelet] Rev. Mat. Iberoamericana 11 (1995), no. 2, 431--451. Multi-resolution analysis of multiplicity d: applications to dyadic interpolation. Appl. Comput. Harmon. Anal. 1 (1994), no. 4, 299--315. Etude d'opérateurs quasi-compacts positifs. Applications aux opérateurs de transfert. (French) [Study of positive quasicompact operators. Applications to transfer operators] Ann. Inst. H. Poincaré Probab. Statist. 30 (1994), no. 3, 437--466. Régularité et conditions de bases de Riesz pour les fonctions d'échelle. (French) [Regularity and the Riesz basis property of scaling functions] C. R. Acad. Sci. Paris Sér. I Math. 315 (1992), no. 10, 1029--1032. Etude d'une équation fonctionnelle matricielle Probabilités, 1--68, Publ. Inst. Rech. Math. Rennes, 1989/90-1, Univ. Rennes I, Rennes, 1991. Other documents: Markov kernels under minorization and modulated drift conditions (with J. Ledoux). (2024) Tweedie-type stability estimates for the invariant probability measures of perturbed Markov chains under drift conditions (with J. Ledoux). Preprint (2022) Quantitative approximation of the invariant distribution of a Markov chain. A new approach. 2022 (with J. Ledoux). Additional material on V-geometrical ergodicity of Markov kernels via finite-rank approximations. 2020 (with J. Ledoux). Additional material on bounds of $\ell^2$-spectral gap for discrete Markov chains with band transition matrices. 2015 (with J. Ledoux). Un théorème de renouvellement. Avec D. Guibourg. Revue de la filière Mathématiques RMS, N.2 (janvier 2016) Espérance de $\max(X_1,\cdots,X_n)$ (Avec D. Guibourg). Revue de la filière Mathématiques RMS, N.4, 111-113 (août 2015) Additional material on local limit theorem for finite Additive Markov Processes (with J. Ledoux), 2013. Quasi-compactness of Markov kernels on weighted-supremum spaces and geometrical ergodicity (with D. Guibourg and J. Ledoux). arXiv:1110.3240, 2011.