Densities for scalar-valued BSDEs via unique continuation and backward uniqueness
with D. Schwarz, preprint, 2026.
Research interests
- Stochastic dynamical systems
- Stein's method and limit theorems
- Malliavin calculus and Gaussian analysis
- Markov diffusion operators and Dirichlet forms
- Random matrices and free probability
- Regularity of laws and PDE methods
- Fractional Brownian motion
Preprints
Uniform-in-time quantitative fluctuations of large scale interacting particle systems
with K. Spiliopoulos, preprint, 2026.
Quantitative fluctuation analysis for continuous-time stochastic gradient descent via Malliavin calculus
with S. Dhama and K. Spiliopoulos, preprint, 2026.
Gaussian approximation on the Skorokhod space via Malliavin calculus and regularization
with S. Campese, preprint, 2025.
Published papers
A caveat on metrizing convergence in distribution on Hilbert spaces
with F. Bassetti, S. Campese and G. Peccati, Statistics & Probability Letters, vol. 233, 6pp., 2026.
Quantitative error bounds for scaling limits of stochastic iterative algorithms
with X. Wang, M. Kasprzak, J. Negrea and J. Huggins, The Annals of Applied Probability, 2026.
Non-central limit of densities of some functionals of Gaussian processes
with T. Dang and Y. Hu, Electronic Journal of Probability, vol. 30, paper no. 181, 40pp., 2025.
Spherical Poisson waves
with C. Durastanti, D. Marinucci and A. Todino, Electronic Journal of Probability, vol. 29, paper no. 8, 27pp., 2024.
Quantitative fluctuation analysis of multiscale diffusion systems via Malliavin calculus
with K. Spiliopoulos, Stochastic Processes and their Applications, vol. 180, paper no. 104524, 34pp., 2025.
Moderate deviation principle for multiscale systems driven by fractional Brownian motion
with T. Dang and K. Spiliopoulos, Journal of Theoretical Probability, vol. 36, paper no. 1, 57pp., 2023.
Functional Gaussian approximations on Hilbert-Poisson spaces
with S. Campese and T. Dang, ALEA, Lat. Am. J. Probab. Math. Stat. 21, 517-553, 2024.
High dimensional regimes of non-stationary Gaussian correlated Wishart matrices
with T. Dang, Random Matrices: Theory and Applications, no. 1, Paper No. 2250006, 43 pp., 2022.
Discrete-time inference for slow-fast systems driven by fractional Brownian motion
with S. Gailus and K. Spiliopoulos, Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal (MMS), vol. 19, no. 3, 1333-1366, 2021.
Limiting behavior of large correlated Wishart matrices with chaotic entries
with C.P. Diez and C.A. Tudor, Bernoulli, vol. 27, no. 2, 1077-1102, 2021.
Typical dynamics and fluctuation analysis of slow-fast systems driven by fractional Brownian motion
with S. Gailus and K. Spiliopoulos, Stochastics and Dynamics, vol. 21, no. 7, Paper No. 2150030, 30pp., 2021.
Approximation of Hilbert-valued Gaussians on Dirichlet structures
with S. Campese, Electronic Journal of Probability, vol. 25, paper no. 150, 30pp., 2020.
Freeness characterizations on free chaos spaces
with I. Nourdin, Pacific Journal of Mathematics, vol. 305, no. 2, 447-472, 2020.
Four moments theorems on Markov chaos
with S. Campese, N. Leonenko and M.S. Taqqu, The Annals of Probability, vol. 47, no. 3, 1417-1446, 2019.
On high-frequency limits of U-statistics in Besov spaces over compact manifolds
with C. Durastanti, Illinois Journal of Mathematics, vol. 61, no. 1-2, 97-125, 2018.
Free quantitative fourth moment theorems on Wigner space
with S. Campese, International Mathematics Research Notices (IMRN), vol. 2018, no. 16, 4969-4990, 2018.
On normal approximations for the two-sample problem on multidimensional tori
with C. Durastanti, Journal of Statistical Planning and Inference, vol. 196, 56-69, 2018.
Vector-valued semicircular limits on the free Poisson chaos
Electronic Communications in Probability, vol. 21, no. 55, 1-11, 2016.
Gaussian approximation of nonlinear statistics on the sphere
with C. Durastanti, D. Marinucci and G. Peccati, Journal of Mathematical Analysis and Applications, vol. 436, no. 2, 1121-1148, 2016.
On the law of the solution to a stochastic heat equation with fractional noise in time
with C.A. Tudor, Random Operators and Stochastic Equations, vol. 23, no. 3, 179-186, 2015.
Poisson convergence on the free Poisson algebra
Bernoulli, vol. 21, no. 4, 2139-2156, 2015.
Semicircular limits on the free Poisson chaos: counterexamples to a transfer principle
with G. Peccati, Journal of Functional Analysis, vol. 267, no. 4, 963-997, 2014.
Portmanteau inequalities on the Poisson space: mixed regimes and multidimensional clustering
with G. Peccati, Electronic Journal of Probability, vol. 19, no. 66, 1-42, 2014.
Density estimates for solutions to one dimensional backward SDE's
with O. Aboura, Potential Analysis, vol. 38, no. 2, 573-587, 2013.
Asymptotic Cramér type decomposition for Wiener and Wigner integrals
with J.C Breton, Infinite Dimensional Analysis, Quantum Probability and Related Topics, vol. 16, no. 1, 1-13, 2013.
Malliavin calculus and self normalized sums
with C.A. Tudor, Séminaire de Probabilités XLV, Lecture Notes in Mathematics, Springer, 323-351, 2013.
Asymptotic theory for fractional regression models via Malliavin calculus
with C.A. Tudor, Journal of Theoretical Probability, vol. 25, no. 2, 536-564, 2012.
Berry-Esséen bounds for long memory moving averages via Stein's method and Malliavin calculus
with C.A. Tudor, Stochastic Analysis and Applications, vol. 29, no. 5, 881-905, 2011.
Cramér's theorem for gamma random variables
with C.A. Tudor, Electronic Communications in Probability, vol. 16, no. 34, 365-378, 2011.
Book chapters
U-statistics on the spherical Poisson space
with C. Durastanti, D. Marinucci and G. Peccati, in Stochastic analysis for Poisson point processes: Malliavin calculus, Wiener-Itō chaos expansions and stochastic geometry, Bocconi & Springer Series, Springer, 2015.
The Malliavin-Stein method on the Poisson space
with G. Peccati, in Stochastic analysis for Poisson point processes: Malliavin calculus, Wiener-Itō chaos expansions and stochastic geometry, Bocconi & Springer Series, Springer, 2015.
Links
- A webpage on Stein's method and Malliavin calculus by Ivan Nourdin.
- A beautiful real-time fluid dynamics simulation solver for Navier-Stokes equations based on the paper Real-Time Fluid Dynamics for Games by Jos Stam.
- Main mathematical journals classification by the Australian Research Council. Another classification based on the impact factor is available here.
- The Erdös Number Project studies research collaboration among mathematicians. A hysterical comic that illustrate this piece of folklore of mathematicians can be found here.
Teaching
M2