S O L E S N E    B O U R G U I N 

Associate Professor Department of Mathematics and Statistics Boston University bourguin@math.bu.edu

665 Commonwealth Avenue Boston, MA 02215 Office CCDS 436 +1 (617) 358 2394

RESEARCH INTERESTS	Stochastic dynamical systems Fractional Brownian motion and related processes Regularity of laws and PDE methods Malliavin calculus, Markov diffusion operators and Dirichlet forms Stein's method and limit theorems Random matrices and free probability theory
TEACHING	Spring 2025 MA242 - Linear Algebra Spring 2025 MA780 - Probability Theory II
SEMINARS	Boston University Statistics and Probability Seminar Series (for scheduled talks). For date availability and past seminars, please see the dedicated page.
RESEARCH	Quantitative error bounds for scaling limits of stochastic iterative algorithms, with X. Wang, M. Kasprzak, J. Negrea and J. Huggins, preprint, 2025. Non-central limit of densities of some functionals of Gaussian processes, with T. Dang and Y. Hu, preprint, 2024. Spherical Poisson waves, with C. Durastanti, D. Marinucci, A. Todino, Electronic Journal of Probability, vol. 29, paper no. 8, 27pp., 2024. [Journal] [arXiv] 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. [Journal] [arXiv] 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. [Journal] [arXiv] Functional Gaussian approximations on Hilbert-Poisson spaces, with S. Campese and T. Dang, ALEA, Lat. Am. J. Probab. Math. Stat. 21, 517-553, 2024. [Journal] [arXiv] 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. [Journal] [arXiv] 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. [Journal] [arXiv] 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. [Journal] [arXiv] 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. [Journal] [arXiv] Approximation of Hilbert-valued Gaussians on Dirichlet structures, with S. Campese, Electronic Journal of Probability, vol. 25, paper no. 150, 30pp., 2020. [Journal] [arXiv] Freeness characterizations on free chaos spaces, with I. Nourdin, Pacific Journal of Mathematics, vol. 305, no. 2, 447-472, 2020. [Journal] [arXiv] 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. [Journal] [arXiv] 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. [Journal] [arXiv] Free quantitative fourth moment theorems on Wigner space, with S. Campese, International Mathematics Research Notices (IMRN), vol. 2018, no. 16, 4969-4990, 2018. [Journal] [arXiv] 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. [Journal] [arXiv] Vector-valued semicircular limits on the free Poisson chaos, Electronic Communications in Probability, vol. 21, no. 55, 1-11, 2016. [Journal] [arXiv] 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. [Journal] [arXiv] 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. [Journal] [arXiv] Poisson convergence on the free Poisson algebra, Bernoulli, vol. 21, no. 4, 2139-2156, 2015. [Journal] [arXiv] 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. [Journal] [arXiv] 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. [Journal] [arXiv] Density estimates for solutions to one dimensional backward SDE's, with O. Aboura, Potential Analysis, vol. 38, no. 2, 573-587, 2013. [Journal] [arXiv] 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. [Journal] [arXiv] Malliavin calculus and self normalized sums, with C.A. Tudor, Séminaire de Probabilités XLV, Lecture Notes in Mathematics, Springer, 323-351, 2013. [Journal] [arXiv] Asymptotic theory for fractional regression models via Malliavin calculus, with C.A. Tudor, Journal of Theoretical Probability, vol. 25, no. 2, 536-564, 2012. [Journal] [arXiv] 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. [Journal] [arXiv] Cramér's theorem for gamma random variables, with C.A. Tudor, Electronic Communications in Probability, vol. 16, no. 34, 365-378, 2011. [Journal] [arXiv]
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.
MATH 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.