Research articles
Bottom of the spectrum for manifolds foliated by minimal leaves, arXiv preprint, 2024
With Quanjun Lang and Yannick Sire: Extension method in Dirichlet spaces with sub-Gaussian estimates and applications to regularity of jump processes on fractals, arXiv preprint, 2024
With Maria Gordina, Rohan Sarkar: Dimension-independent functional inequalities by tensorization and projection arguments, arXiv preprint, 2024
With Patricia Alonso Ruiz: Korevaar-Schoen p-energies and their Γ-limits on Cheeger spaces, arXiv preprint, 2024
With Celine Lacaux: Fractional Stable random fields on the Sierpinski gasket, arXiv preprint, 2024
With Li Chen, Che-Hung Huang, Cheng Ouyang, Samy Tindel, Jing Wang: Parabolic Anderson model in bounded domains of recurrent metric measure spaces, arXiv preprint, 2024
With Li Chen: Heat kernel gradient estimates for the Vicsek set, arXiv preprint 2023,
With Maria Gordina, David Herzog, Jina Kim, Tai Melcher: Functional inequalities for a family of infinite-dimensional diffusions with degenerate noise, arXiv preprint 2023
With Patricia Alonso Ruiz: Dirichlet forms on metric measure spaces as Mosco limits of Korevaar-Schoen energies, arXiv preprint 2023, To appear in The Annali della Scuola Normale Superiore di Pisa, 2024
With Nizar Demni, Jing Wang: Stochastic areas, Horizontal Brownian Motions, and Hypoelliptic Heat Kernels, arXiv preprint 2022, Book to appear in the EMS Tract collection
With Erlend Grong, Rob Neel, Anton Thalmaier: Variations of the sub-Riemannian distance on Sasakian manifolds with applications to coupling, arXiv preprint 2022
Korevaar-Schoen-Sobolev spaces and critical exponents in metric measure spaces, arXiv preprint, 2022
With Li Chen: Sobolev spaces and Poincaré inequalities on the Vicsek fractal, arXiv preprint, 2022, To appear in Ann. Fenn. Math.
With Cheng Ouyang, Samy Tindel, Jing Wang: Parabolic Anderson model on Heisenberg groups: the Itô setting, arXiv preprint, 2022,to appear in JFA
With Patricia Alonso Ruiz: Oscillations of BV measures on nested fractals, arXiv preprint, 2022, To appear in Journal of Fractal Geometry
With Li Chen: Dirichlet fractional Gaussian fields on the Sierpinski gasket and their discrete graph approximations, arXiv preprint, 2022, to appear in SPA
With Erlend Grong, and Sylvie Vega Molino, A horizontal Chern-Gauss-Bonnet formula on totally geodesic foliations, arXiv preprint, 2021, To appear in AGAG
With Nizar Demni, Jing Wang: Generalized stochastic areas, Winding numbers, and hyperbolic Stiefel fibrations, arXiv preprint, 2021,To appear in Int. Math. Res. Notices
With Maria Gordina and Tai Melcher: Quasi-invariance for infinite-dimensional Kolmogorov diffusions, arXiv preprint 2021,
With Gunhee Cho and Guang Yang: A note on first eigenvalue estimates by coupling methods in Kähler and quaternion Kähler manifolds, arXiv preprint, 2021, To appear in ECP
With Patricia Alonso Ruiz: Yet another characterizarion of BV functions on Riemannian manifolds, arXiv preprint, 2020, To appear in Annales de La Faculte des Sciences de Toulouse
With Quanjun Lang and Yannick Sire: Powers of generators on Dirichlet Spaces and applications to Harnack principles, arXiv preprint, 2020
With Jing Wang: Asymptotic windings of the block determinants of a unitary Brownian motion and related diffusions, 2020, arXiv preprint, To appear in Electronic Journal of Probability
With Nate Eldredge: Transportation inequalities for Markov kernels and their applications, arXiv preprint, 2020, To appear in Electronic Journal of Probability
With Gunhee Cho: The subelliptic heat kernel of the octonionic anti-de Sitter Fibration, arXiv preprint, 2020, To appear in Sigma 2021
With Li Chen: A note on second order Riesz transforms in 3-dimensional Lie groups, arXiv preprint 2020, Arkiv der Math, 2022
With Guang Yang: Brownian motions and heat kernel lower bounds on Kahler and quaternion Kahler manifolds, arXiv preprint, To appear in International Mathematical Research Notices, 2020
With Celine Lacaux: Fractional Gaussian fields on the Sierpinski gasket and related fractals, arXiv preprint, To appear in Journal d'Analyse Mathematique, 2020
With Rodrigo Banuelos, Li Chen, Yannick Sire: Multiplier theorems via martingale transforms, arXiv preprint, 2020, to appear in Journal of Functional Analysis
With Erlend Grong, Kazumasa Kuwada, Rob Neel, Anton Thalmaier: Radial processes for sub-Riemannian Brownian motions and applications, To appear in Electronic Journal of Probability, arXiv preprint, 2020
With Patricia Alonso-Ruiz: Gagliardo-Nirenberg, Trudinger-Moser and Morrey inequalities on Dirichlet spaces, arXiv preprint, To appear in Journal of Mathematical Analysis & Applications, 2020
With Patricia Alonso-Ruiz, Li Chen, Luke Rogers, Nageswari Shanmugalingam, Alexander Teplyaev: BV functions and fractional Laplacians on Dirichlet spaces, arXiv preprint, 2019
With Erlend Grong, Sylvie Vega Molino, Luca Rizzi: Comparison theorems on H-type sub-Riemannian manifolds, arXiv preprint, 2019
With Maria Gordina, David Herzog: Gamma calculus beyond Villani and explicit convergence estimates for Langevin dynamics with singular potentials, 2019, arXiv preprint, ARMA, 2021
With Nizar Demni, Jing Wang: Quaternionic Brownian windings, To appear in Journal of Theoretical Probability, 2019, arXiv preprint
With Michel Bonnefont, Li Chen: Convergence to equilibrium for hypoelliptic non-symmetric Ornstein-Uhlenbeck type operators, arXiv preprint
With Ovidiu Munteanu: Improved Beckner-Sobolev inequalities on K\"ahler manifolds, 2019, Arxiv preprint, To appear in Journal of Geometric Analysis
With Qi Feng, Cheng Ouyang: Density of the signature process of fBm, 2019, Arxiv preprint, To appear in the Transactions of the AMS, 2020
With Gunhee Cho: The subelliptic heat kernel of the octonionic Hopf fibration, 2019, Arxiv preprint, To appear in Potential Analysis
With Patricia Alonso-Ruiz, Li Chen, Luke Rogers, Nageswari Shanmugalingam, Alexander Teplyaev: Besov class via heat semigroup on Dirichlet spaces III: BV functions and sub-Gaussian heat kernel estimates, 2018, Arxiv preprint
With Nizar Demni, Jing Wang: Quaternionic stochastic areas, 2019, To appear in Stoch. Proc. & Appl. Arxiv preprint
With Erlend Grong, Sylvie Vega Molino, Luca Rizzi: H-type foliations, 2018, Arxiv preprint, To appear in Diff. Geom. and its Applications
With Patricia Alonso-Ruiz, Li Chen, Luke Rogers, Nageswari Shanmugalingam, Alexander Teplyaev: Besov class via heat semigroup on Dirichlet spaces II: BV functions and Gaussian heat kernel estimates, 2018, accepted for publication in Cal. Var. PDE, Arxiv preprint
With Patricia Alonso-Ruiz, Li Chen, Luke Rogers, Nageswari Shanmugalingam, Alexander Teplyaev: Besov class via heat semigroup on Dirichlet spaces I: Sobolev type inequalities, 2018, to appear in Jour. Func. Anal., Arxiv preprint
With Maria Gordina, Phanuel Mariano: On the Cheng-Yau gradient estimate for Carnot groups and sub-Riemannian manifolds, Arxiv preprint, Proceedings of the AMS, Volume 147, Number 7, July 2019, Pages 3181–3189
With Ayelet Amiran, Skylyn Brock, Berend Coster, Ryan Craver, Ugonna Ezeaka, Phanuel Mariano, Mary Wishart: The financial value of knowing the distribution of stock prices in discrete market models, (2018), arXiv preprint, to appear in Involve
With Patricia Alonso-Ruiz, Li Chen, Luke Rogers, Nageswari Shanmugalingam, Alexander Teplyaev: BV functions and Besov spaces associated with Dirichlet spaces, 2018, not submiited book draft, Arxiv preprint
With Nizar Demni, Jing Wang: The horizontal heat kernel on the quaternionic anti de-Sitter spaces and related twistor spaces, 2018, To appear in Potential Analysis, Arxiv preprint
With Maria Gordina, Phanuel Mariano: Gradient Bounds for Kolmogorov Type Diffusions, 2018, Arxiv preprint, To appear in Annales de l'IHP
With Nizar Demni: Integral representation of the subelliptic heat kernel on the complex anti-de Sitter fibration, To appear in Archiv der Math, 2018, Arxiv preprint
With Rodrigo Banuelos, Li Chen: Gundy-Varopoulos martingale transforms and their projection operators on manifolds and vector bundles, 2018, Arxiv preprint, To appear in Math. Annalen
Geometric Inequalities on Riemannian and sub-Riemannian manifolds by heat semigroups techniques, 2018, Arxiv preprint, Levico Summer School lectures on analysis on metric spaces, to appear
With Erlend Grong: Transverse Weitzenb\"ock formulas and de Rham cohomology of totally geodesic foliations, 2017, Arxiv preprint, To appear in Annals of Global Analysis and Geometry, 2019
With Qi Feng, Maria Gordina: Integration by parts and quasi-invariance for the horizontal Wiener measure on a foliated compact manifold, 2017, Arxiv preprint, To appear in Journal of Functional Analysis, 2019
With Erlend Grong, Kazumasa Kuwada, Anton Thalmaier: Sub-Laplacian comparison theorems on totally geodesic Riemannian foliations, 2017, Arxiv preprint, To appear in Cal. Var & PDE, 2019
With Camille Tardif: Hypocoercive estimates on foliations and velocity spherical Brownian motion, Kinet. Relat. Models 11 (2018), no. 1, 1–23, Arxiv preprint
With Daniel J. Kelleher: Differential forms on Dirichlet spaces and Bakry-\'Emery estimates on metric graphs, Transactions of the AMS, Volume 371, Number 5, 1 March 2019, Pages 3145–3178, Arxiv preprint
With Jing Wang: Stochastic areas, Windings and Hopf fibrations, Probab. Theory Related Fields 169 (2017), no. 3-4, 977–1005., Arxiv preprint
Wasserstein contraction properties for hypoellliptic diffusions, 2016, Lecture Notes, Arxiv preprint
With Michel Bonnefont, Reverse Poincare inequalities, Isoperimetry and Riesz transforms in Carnot groups, 2015, Arxiv preprint, Nonlinear Anal. 131 (2016), 48–59.
With Qi Feng, Log-Sobolev inequalities on the horizontal path space of a totally geodesic foliation, 2015, Arxiv preprint
With Michel Bonnefont, Curvature-dimension estimates for the Laplace-Beltrami operator of a totally geodesic foliation, Arxiv preprint, Nonlinear Anal. 126 (2015), 159–169
Sub-Laplacians and hypoelliptic operators on totally geodesic Riemannian foliations, Geometry, analysis and dynamics on sub-Riemannian manifolds. Vol. 1, 259–321, EMS Ser. Lect. Math., Eur. Math. Soc., Zürich, 2016, Arxiv preprint
With Bumsik Kim and Jing Wang: Transverse Weitzenbock formulas and curvature dimension inequalities on Riemannian foliations with totally geodesic leaves, Comm. Anal. Geom. 24 (2016), no. 5, 913–937, Arxiv preprint
With Bumsik Kim: The Lichnerowicz-Obata theorem on sub-Riemannian manifolds with transverse symmetries, 2014, Arxiv preprint, J. Geom. Anal. 26 (2016), no. 1, 156–170.
With Cheng Ouyang: On small time asymptotics for rough differential equations driven by fractional Brownian motions, 2015, Arxiv preprint, Large deviations and asymptotic methods in finance, 413–438, Springer Proc. Math. Stat., 110, Springer, Cham, 2015
Stochastic differential equations driven by loops, Symposium on Probability and Stochastic Processes, 59–80, Progr. Probab., 69, Birkhäuser/Springer, Cham, 2015., Arxiv preprint
Stochastic analysis on sub-Riemannian manifolds with transverse symmetries, Ann. Probab. 45 (2017), no. 1, 56–81. Arxiv preprint
With Eulalia Nualart, Cheng Ouyang, Samy Tindel: On probability laws of differential systems driven by fractional Brownian motions, Ann. Probab. 44 (2016), no. 4, 2554–2590, Arxiv preprint
With Jing Wang: The subelliptic heat kernels of the quaternionic Hopf fibration, Potential Analysis, 41, no 3, 959-982, (2014) Arxiv preprint
With Rodrigo Banuelos: Trace asymptotics for subordinate semigroups, 2013 , Arxiv preprint
Bakry-Emery meet Villani, J. Funct. Anal. 273 (2017), no. 7, 2275–2291, Arxiv preprint,
With Cheng Ouyang and Xuejing Zhang: Varadhan estimates for rough differential equations driven by fractional Brownian motions, 2013, Arxiv preprint, Stochastic Process. Appl. 125 (2015), no. 2, 634–652.
With Cheng Ouyang and Xuejing Zhang: Smoothing effect of rough differential equations driven by fractional Brownian motions, 2013, Arxiv preprint, Ann. Inst. Henri Poincaré Probab. Stat. 52 (2016), no. 1, 412–428.
With Matthew Cecil: The subelliptic heat kernel on the three-dimensional solvable groups, 2013, Arxiv preprint, Forum Math. 27 (2015), no. 4, 2051–2086.
With Jing Wang: Curvature dimension inequalities and subelliptic heat kernel gradient bounds on contact manifolds, Potential Analysis, 40, 2014, 163-193, Arxiv preprint
With Michel Bonnefont, Nicola Garofalo, Isidro H. Munive: Volume and distance comparison theorems for sub-Riemannian manifolds, Arxiv preprint, J. Funct. Anal. 267 (2014), no. 7, 2005–2027.
With Bumsik Kim: Sobolev, Poincare and isoperimetric inequalities for subelliptic diffusion operators satisfying a generalized curvature dimension inequality, Revista Matematica Iberoamericana, 30, (2014), 1, 109-131, arXiv preprint
Diffusion processes and stochastic calculus, 285 pages, EMS textbooks in mathematics. European Mathematical Society (EMS), Zürich, 2014. xii+276 pp. ISBN: 978-3-03719-133-0
With Jing Wang: The subelliptic heat kernel on the CR sphere, Math. Z., 275, (2013), 1-2, 135-150, Arxiv preprint
With Xuejing Zhang: Taylor expansion for the solution of a stochastic differential equation driven by fractional Brownian motions, Electronic Journal of Probability, Volume 17, Article 51, 1-21, 2012 Link to the article
With Michel Bonnefont: Sub-Riemannian balls in CR Sasakian manifolds, Proceedings of the AMS, 141, (2013), no 11, 3919-3924, Arxiv preprint
With Rodrigo Banuelos: Martingale transforms and their projection operators on manifolds , Potential Analysis, 38, (2013), no 4, 1071-1089, Arxiv preprint
With Maria Gordina and Tai Melcher: Quasi-invariance for heat kernel measures on sub-Riemannian infinite-dimensional Heisenberg groups, Transactions of the AMS, 365, (2013), no 8, 4313-4350, Arxiv preprint
With Michel Bonnefont: Log-Sobolev inequalities for subelliptic operators satisfying a generalized curvature dimension inequality, 2011, Arxiv preprint , Journal of Functional Analysis, Volume 262, Issue 6, 2646-2676, 2012.
With Nicola Garofalo: A note on boundedness of Riesz transform for some subelliptic operators, Arxiv preprint,International Mathematics Research Notices, (2013), no 2, 398-421 .
With Cheng Ouyang and Samy Tindel: Upper bounds for the density of solutions of stochastic differential equations driven by fractional Brownian motions, Annales de l'IHP, (50), 2014, 111-135, Arxiv preprint
With Cheng Ouyang: Gradient Bounds for Solutions of Stochastic Differential Equations Driven by Fractional Brownian Motions, 2011, Proceedings in honor of Pr. Nualart's 60th birthday, Arxiv preprint
With Nicola Garofalo: Curvature-dimension inequalities and Ricci lower bounds for sub-Riemannian manifolds with transverse symmetries, Journal of the EMS, Vol. 19, Issue 1, 2017, Arxiv preprint
With Alice Vatamanelu: A note on lower bounds estimates for the Neumann eigenvalues of manifolds with positive Ricci curvature, Potential Analysis, 37, (2012), no 1, 91-101, Arxiv preprint
With Michel Bonnefont and Nicola Garofalo: A sub-Riemannian curvature-dimension inequality, volume doubling property and the Poincare inequality, Math. Ann. 358 (2014), 3-4, 833-860, Arxiv preprint
With Cheng Ouyang: Small-time kernel expansion for solutions of stochastic differential equations driven by fractional Brownian motions, Stochastic Processes and their Applications, Volume 121, Issue 4, April 2011, Pages 759-792, Arxiv preprint
With Nicola Garofalo: Perelman's entropy and doubling property on Riemannian manifolds, Journal of Geometric Analysis, 21, 1119-1131, 2011, Arxiv preprint
Stochastic Taylor expansions and heat kernels asymptotics, ESAIM: Probability and Statistics/ Volume 16/ January 2012, pp. 453-478, Arxiv preprint
With N. O'Connell: Exponential functionals of Brownian motion and class one Whittaker functions, Annales de l'IHP, Probabilites et Statistique, Vol.47, 1096-1120, (2011), Arxiv preprint
With D. Bakry, Michel Bonnefont, B. Qian : Subelliptic Li-Yau estimates on three dimensional model spaces Arxiv preprint , Potential Theory and Stochastics in Albac, Aurel Cornea Memorial Volume (2009).
Stochastic processes, in The International Encyclopedia of Education, 3rd Edition, edited by Barry McGaw, Penelope Peterson and Eva Baker, Elsevier (2009).
With Michel Bonnefont: The subelliptic heat kernel on SU(2): Representations, Asymptotics and Gradient bounds Arxiv Preprint, Math. Zeit., Volume 263, Issue 3, Pages 647-672, (2009).
With Martin Hairer, Josef Teichmann: Ornstein-Uhlenbeck processes on Lie groups, Arxiv preprint, Journal of Functional Analysis, Volume 255, Issue 4, Pages 877-890, (2008).
With D. Bakry, M. Bonnefont, D. Chafai: On gradient bounds for the heat kernel on the Heisenberg group Preprint, Journal of Functional Analysis, Volume 255, Issue 8, pp. 1905-1938 (2008).
Chen series and Atiyah-Singer theorem, Journal of Functional Analysis, Vol. 254, 2, pp. 301-317 (2008). Link
Self-similarity and fractional Brownian motion on Lie groups, Arxiv Preprint, Electronic Journal of Probability, Vol. 13, pp. 1120-1139, (2008).
With Martin Hairer: A version of Hormander's theorem for the fractional Brownian motion, Arixv Preprint, Prob. The. Rel. Fields., 139, 373-395, (2007).
With Laure Coutin: Operators associated with a stochastic differential equation driven by fractional brownian motions, Arxiv Preprint, Stochastic Processes and their Applications, 117, Issue 5, pp. 550-574, (2007).
With Laure Coutin: Volterra Bridges and non-canonical Representations, Markov processes and related fields, Vol. 13, Issue 3, pp. 587-596, (2007). Link
With David Nualart: Notes on the two-dimensional fractional Brownian motion, Annals of Probability, 2006, Vol. 34, 1, 159-180. Link
With Laure Coutin: Etude en temps petit du flot d'equations conduites par des mouvements browniens fractionnaires, in French, Note CRAS, Ser. I 341, 39-42, (2005). Link
With Josef Teichmann: Hypoellipticity in infinite dimensions and an application in interest rate theory, Annals of Applied Probability, 2005, Vol. 15, 3, 1765-1777. Link
With David Nualart: Equivalence of Volterra Processes, Stochastic Processes and Their Applications, Vol. 107, 327-350 (2003).Link
A Bismut type theorem for subelliptic semigroups, CRAS, 2007, Vol. 34, 12, pp. 765
An Introduction to the geometry of stochastic flows, Imperial College Press, 140pp, (2005).
The tangent space to a hypoelliptic diffusion and applications, Seminaire de Probabilites,Vol. XXXVIII, LNM 1857, Springer, (2005).
Equations differentielles stochastiques conduites par des lacets dans les groupes de Carnot, in French, CRAS serie I338, (2004) 719-722.
Conditioning and Initial Enlargement of Filtration on a Riemannian Manifold, Annals of Probability, Vol. 32, 3A, 2286-2303, (2004). Link
Skew-product decompositions of Brownian motions on manifolds: A probabilistic aspect of Lichnerowicz-Szabo theorem, Bulletin des Sciences Mathematiques, Vol. 126, 481-491, (2002). Link
With Michele Thieullen: Pinning Class of the Wiener Measure by a Functional: Related Martingales and Invariance Properties, Probability Theory and Related Fields, Vol. 127, 1-36 (2003), Link
With Laurent Nguyen-Ngoc: The Financial Value of a Weak Information, Finance and Stochastics, 8, pp. 415-435, (2004). Link
Modelling Anticipations on a Financial Market, In Paris-Princeton Lectures on Mathematical Finance, Springer, LNM 1814, (2003) Link
Conditioned Stochastic Differential Equations and Application to Finance, Stochastic Processes and their Applications, Vol. 100, 109-145, (2002), Link.
Further Exponential Generalization of Pitman's 2M-X theorem, Electronic Communications in Probability, Vol. 7, 37-46, (2002), Link.
With Nicolas Gaussel. Badly Arbitraged Markets and Negative Martingale Measures