# Prof. Dr. Ivan Nourdin

### Full professor in Mathematics - area : sochastic modelling

Discipline(s) Mathematics
Sujets de recherche Functional inequalities, Stein's method, Mathematics of sparsity, Rough paths theory, Free probabililty, Malliavin calculus
Faculté ou Centre Faculté des Sciences, des Technologies et de Médecine
Department Département Mathématiques
Maison du Nombre
6, Avenue de la Fonte
L-4364 Esch-sur-Alzette
Bureau sur le campus MNO, E05 0515-090
E-mail
Téléphone (+352) 46 66 44 6380
Fax (+352) 46 66 44 36380
Réseaux sociaux & blogs
Langues parlées English, French
Séjours de recherche en France, Luxembourg, USA

Prof. Dr. Ivan Nourdin (born 1978) studied mathematics at the Université de Lorraine and at the École Normale Supérieure de Cachan, France.

In 2004, he received the PhD from the Université de Lorraine, France.

He joined the Université Pierre et Marie Curie (Paris VI) as an assistant professor in 2005 and then the Université de Lorraine as a full professor in 2010.

In 2011, he was awarded the Annual Prize of the Fondation des Sciences Mathématiques de Paris.

In 2013, he was awarded the France Scopus Researcher Award in the field of Mathematics by Elsevier.

He was appointed professor of stochastic modelling at the University of Luxembourg in March 2014, where he is currently building a research group.

In 2015, together with Giovanni Peccati he was awarded the FNR Award for Outstanding Scientific Publication (for the book "Normal Approximations with Malliavin Calculus: from Stein's method to universality", published by Cambridge University Press in 2012).

His research interests include Malliavin calculus, Stein's method, functional inequalities, free probability, rough paths theory, and inference for high-dimensional problems.

Ivan Nourdin is author/coauthor of more than 80 publications in international scientific journals as well as 2 monographs.

Last updated on: mardi 14 novembre 2017

#### Education - Universities attended

• 2008: Habilitation to Drive Research, University of Paris VI, France
• 2001 - 2004: PhD student, University of Nancy I, France
• 2000: Agrégation de mathématiques, ranked 18th .
• 1999 – 2001: Student at the École Normale Supérieure de Cachan

#### Current Position

• Full Professor, Faculty of Science, Technology and Communication, Luxembourg University, since 2014

#### Previous employment

•  Full Professor, Université de Lorraine, 2010-2014
•  On leave at the Laboratoire de Probabilités et Modèles Aléatoires (Université Paris VI and VII) thanks to the Prize of the Fondation des Sciences Mathématiques de Paris, 2011-2012
•  Maître de Conférences, Université Paris VI, 2005-2010
•  Attaché Temporaire d'Enseignement et de Recherche, École des Mines de Nancy, 2004-2005
•  Moniteur, Université Nancy I, 2001-2004
• Student (with salary), École Normale Supérieure de Cachan, 1999-2001

#### Honours

• Winner of the 2015 FNR Researcher Award for Outstanding Scientific Publication
• Winner of the 2013 France Scopus Researcher Award in the field of Mathematics
• Winner of the 2011 Prize of the Fondation des Sciences Mathématiques de Paris

Last updated on: 19 avr 2016

• Guangqu Zheng, Université du Luxembourg, 2015-2018
• Tran Thi Thanh Diu, Université du Luxembourg, 2015-2018
• Rola Zintout, Université de Lorraine, 2012-2015
• Raghid Zeineddine, Université de Lorraine, 2011-2014
• Salim Noreddine, Université Paris VI, 2009-2013

Last updated on: 06 nov 2017

# Sous presse

Concentration of the Intrinsic Volumes of a Convex Body
; ; ; ;

in Geometric Aspects of Functional Analysis (in press)

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# 2021

Limit theorems for integral functionals of Hermite-driven processes
; ; ;

in Bernoulli (2021), 27(3), 1764-1788

Approximation of Fractional Local Times: Zero Energy and Derivatives
; ;

in Annals of Applied Probability (2021), In press

Local times and sample path properties of the Rosenblatt process
; ; ;

in Stochastic Processes and Their Applications (2021), 131

The Breuer-Major Theorem in total variation: improved rates under minimal regularity
; ;

in Stochastic Processes and Their Applications (2021), 131

Gaussian fluctuation for Gaussian Wishart matrices of overall correlation
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E-print/Working paper (2021)

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# 2020

Estimating the number of infected persons
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E-print/Working paper (2020)

Freeness characterisations on free chaos spaces
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in Pacific Journal of Mathematics (2020), 305(2), 447-472

Continuous Breuer-Major theorem: tightness and non-stationarity
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in Annals of Probability (2020), 48(1), 147-177

Stein's method for asymmetric alpha-stable distributions, with application to the stable CLT
; ;

in Journal of Theoretical Probability (2020)

Small Scale CLTs for the Nodal Length of Monochromatic Waves
; ; ;

E-print/Working paper (2020)

Asymptotic error distribution for the Riemann approximation of integrals driven by fractional Brownian motion
; ;

E-print/Working paper (2020)

The functional Breuer-Major theorem
;

in Probability Theory and Related Fields (2020), 176

Multivariate normal approximation on the Wiener space: new bounds in the convex distance
; ;

E-print/Working paper (2020)

Restricted hypercontractivity on the Poisson space
; ;

in Proceedings of the American Mathematical Society (2020), 148

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# 2019

Almost sure limit theorems on Wiener chaos: the non-central case
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in Electronic Communications in Probability (2019), 24(9), 1-12

Multivariate stable approximation in Wasserstein distance by Stein's method
; ; ;

E-print/Working paper (2019)

Non-integrable stable approximation by Stein's method
; ; ; ;

E-print/Working paper (2019)

Phase singularities in complex arithmetic random waves
; ; ;

in Electronic Journal of Probability (2019), 24(71), 1-45

Nodal Statistics of Planar Random Waves
; ;

in Communications in Mathematical Physics (2019), 369(1), 99-151

Berry-Esseen bounds in the Breuer-Major CLT and Gebelein's inequality
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in Electronic Communications in Probability (2019), 24(34), 1-12

Statistical inference for Vasicek-type model driven by Hermite processes
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in Stochastic Processes and Their Applications (2019), 129(10), 3774-3791

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# 2018

Weak symmetric integrals with respect to the fractional Brownian motion
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in Annals of Probability (2018), 46(4), 2243-2267

Convergence of random oscillatory integrals in the presence of long-range dependence and application to homogenization
; ; ;

in Probability and Mathematical Statistics (2018), 38(2), 271-286

Sojourn time dimensions of fractional Brownian motion
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E-print/Working paper (2018)

Asymptotic behaviour of large Gaussian correlated Wishart matrices
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E-print/Working paper (2018)

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# 2017

Gaussian Phase Transitions and Conic Intrinsic Volumes: Steining the Steiner Formula
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in Annals of Applied Probability (2017), 27(1), 1-47

A Stein deficit for the logarithmic Sobolev inequality
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in Science China Mathematics (2017), 60

Exchangeable pairs on Wiener chaos
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in High-Dimensional Probability VIII Proceedings (2017)

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# 2016

Multivariate Gaussian approxi- mations on Markov chaoses
; ; ;

in Electronic Communications in Probability (2016), 21

Convergence of random oscillatory integrals in the presence of long-range dependence and application to homogenization
; ; ;

in Probability and Mathematical Statistics (2016)

Squared chaotic random variables: new moment inequalities with applications
; ; ;

in Journal of Functional Analysis (2016), 270(2), 649-670

Fisher information and the Fourth Moment Theorem
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in Annales de l'Institut Henri Poincare (B) Probability & Statistics (2016), 52(2), 849-867

Quantitative stable limit theorems on the Wiener space
; ;

in Annals of Probability (2016), 44(1), 1-41

Strong asymptotic independence on Wiener chaos
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in Proceedings of the American Mathematical Society (2016), 144(2), 875-886

Classical and free fourth moment theorems: universality and thresholds
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in Journal of Theoretical Probability (2016), 29(2), 653-680

Multidimensional limit theorems for homogeneous sums : a general transfer principle
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in ESAIM: Probability and Statistics (2016), 20

Asymptotic behaviour of the cross-variation of some integral long memory processes
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in Probability and Mathematical Statistics (2016), 36(1),

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# 2015

Local universality of the number of zeros of random trigonometric polynomials with continuous coefficients
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E-print/Working paper (2015)

Stein's method, logarithmic Sobolev and transport inequalities
; ;

in Geometric and Functional Analysis (2015), 25

The optimal fourth moment theorem
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in Proceedings of the American Mathematical Society (2015), 143(7), 3123-3133

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# 2014

Invariance principles for homogeneous sums of free random variables
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in Bernoulli (2014), 20(2), 586-603

Entropy and the fourth moment phenomenon
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in Journal of Functional Analysis (2014), 266(5), 3170-3207

Integration by parts and representation of information functionals
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in Abstract book of 2014 IEEE International Symposium on Information Theory (ISIT) (2014)

Comparison inequalities on the Wiener space
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in Stochastic Processes & Their Applications (2014), 124(4), 1566-1581

Asymptotic independence of multiple Wiener-Itô integrals and the resulting limit laws
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in Annals of Probability (2014), 42(2), 497-526

Central and non-central limit theorems in a free probability setting
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in Journal of Theoretical Probability (2014), 27(1), 220-248

An Itô's type formula for the fractional Brownian motion in Brownian time
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in Electronic Journal of Probability (2014), 19(99), 1-15

Two properties of vectors of quadratic forms in Gaussian random variables
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in Teoriya Veroyatnostei i ee Primeneniya (2014), 59(2), 214-232

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# 2013

Fourth moment theorem and q-Brownian chaos
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in Communications in Mathematical Physics (2013), 321(1), 113-134

Parameter estimation for alpha-fractional bridges
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in Malliavin calculus and stochastic analysis (2013)

Lectures on Gaussian approximations with Malliavin calculus

in Lecture notes in Mathematics (2013)

Absolute continuity and convergence of densities for random vectors on Wiener chaos
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in Electronic Journal of Probability (2013), 18(22), 1--19

Poisson approximations on the free Wigner chaos
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in Annals of Probability (2013), 41(4), 2709--2723

Multidimensional semicircular limits on the free Wigner chaos
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in The Ascona Proceedings, 2011 (2013)

Convergence in total variation on Wiener chaos
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in Stochastic Processes & Their Applications (2013), 123

An invariance principle under the total variation distance
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in Stochastic Processes & Their Applications (2013)

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# 2012

Optimal Berry-Esseen rates on the Wiener space: the barrier of third and fourth cumulants
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in Latin American Journal of Probability and Mathematical Statistics (2012), 9(2), 473--500

Convergence of Wigner integrals to the tetilla law
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in ALEA: Latin American Journal of Probability and Mathematical Statistics (2012), 9

Wigner chaos and the fourth moment
; ; ;

in Annals of Probability (2012), 40(4), 1577--1635

Selected aspects of fractional Brownian motion

Normal approximations with Malliavin calculus
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Convergence in law in the second Wiener/Wigner chaos
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in Electronic Communications in Probability (2012), 17(36),

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# 2011

On the Gaussian approximation of vector-valued multiple integrals
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in Journal of Multivariate Analysis (2011), 102(6), 1008-1017

Yet another proof of the Nualart-Peccati criterion

in Electronic Communications in Probability (2011), 16

Quantitative Breuer-Major theorems
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in Stochastic Processes & Their Applications (2011), 121(4), 793--812

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# 2010

Weak approximation of a fractional SDE
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in Stochastic Processes & Their Applications (2010), 120

Almost sure central limit theorems on the Wiener space
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in Stochastic Processes & Their Applications (2010), 120

Limit theorems for nonlinear functionals of Volterra processes via white noise analysis
; ;

in Bernoulli (2010), 16(4), 1262-1293

Central limit theorems for multiple Skorohod integrals
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in Journal of Theoretical Probability (2010), 23(1), 39-64

Central and non-central limit theorems for weighted power variations of fractional Brownian motion
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in Annales de l'Institut Henri Poincare (B) Probability & Statistics (2010), 46(4), 1055-1079

Stein's method meets Malliavin calculus: a short survey with new estimates
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in Recent development in stochastic dynamics and stochastic analysis (2010)

Universal Gaussian fluctuations of non-Hermitian matrix ensembles: from weak convergence to almost sure CLTs
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in Latin American Journal of Probability and Mathematical Statistics (2010), 7

Cumulants on the Wiener space
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in Journal of Functional Analysis (2010), 258(11), 3775--3791

Multivariate normal approximation using Stein's method and Malliavin calculus
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in Annales de l'Institut Henri Poincare (B) Probability & Statistics (2010), 46(1), 45--58

Stein's method and stochastic analysis of Rademacher functionals
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in Electronic Journal of Probability (2010), 15

Invariance principles for homogeneous sums: universality of Gaussian Wiener chaos
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in Annals of Probability (2010), 38(5), 1947--1985

The weak Stratonovich integral with respect to fractional Brownian motion with Hurst parameter H=1/6
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in Electronic Journal of Probability (2010), 15

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# 2009

Exact confidence intervals for the Hurst parameter of a fractional Brownian motion
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in Electronic Journal of Statistics (2009), 3

Differentiating $\sigma$-fields for Gaussian and shifted Gaussian processes
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in Stochastics (2009), 81(1), 79--97

Milstein's type schemes for fractional SDEs
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in Annales de l'Institut Henri Poincare (B) Probability & Statistics (2009), 45(4), 1085-1098

Trees and asymptotic developments for fractional stochastic differential equations
; ; ;

in Annales de l'Institut Henri Poincare (B) Probability & Statistics (2009), 45(1), 157-174

Stein's method on Wiener chaos
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in Probab. Theory Related Fields (2009), 145(1-2), 75--118

Noncentral convergence of multiple integrals
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in Annals of Probability (2009), 37(4), 1412--1426

Stein's method and exact Berry-Esseen asymptotics for functionals of Gaussian fields
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in Annals of Probability (2009), 37(6), 2231--2261

Second order Poincaré inequalities and CLTs on Wiener space
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in Journal of Functional Analysis (2009), 257(2), 593--609

Asymptotic behavior of weighted quadratic variations of fractional Brownian motion: the critical case H=1/4
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in Annals of Probability (2009), 37(6), 2200-2230

Density formula and concentration inequalities with Malliavin calculus
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in Electronic Journal of Probability (2009), 14

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# 2008

Error bounds on the non-normal approximation of Hermite power variations of fractional Brownian motion
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in Electronic Communications in Probability (2008), 13

Asymptotic expansions at any time for fractional scalar SDEs of Hurst index H>1/2
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in Bernoulli (2008), 14(3), 822-837

Stochastic volatility: approximation and goodness-of-fit test
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in Probability and Mathematical Statistics (2008), 28(1), 1-19

Optimal control for rough differential equations
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in Stochastics & Dynamics (2008), 8(1), 23-33

Exact rate of convergence of some approximation schemes associated to SDEs driven by a fractional Brownian motion
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in Journal of Theoretical Probability (2008), 20(4), 871-899

Delay equations driven by rough paths
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in Electronic Journal of Probability (2008), 13

Weighted power variations of iterated Brownian motion
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in Electronic Journal of Probability (2008), 13

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# 2007

Stochastic derivatives for fractional diffusions
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in Annals of Probability (2007), 35(5), 1998-2020

Dynamical properties and characterization of gradient drift diffusions
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in Electronic Communications in Probability (2007), 12

Correcting Newton-Cotes integrals by Lévy areas
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in Bernoulli (2007), 13(3), 695-711

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# 2006

On the absolute continuity of one-dimensional SDEs driven by a fractional Brownian motion
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in Statistics and Probability Letters (2006), 76(9), 907-912

On the absolute continuity of Lévy processes with drift
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in Annals of Probability (2006), 34(3), 1035-1051

Some linear fractional stochastic equations
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in Stochastics : An International Journal of Probability & Stochastic Processes (2006), 78(2), 51-65

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# 2005

m-order integrals and generalized Itô's formula; the case of a fractional Brownian motion with any Hurst index
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in Annales de l'Institut Henri Poincare (B) Probability & Statistics (2005), 41(4), 781-806

Itô's and Tanaka's type formulae for the stochastic heat equation: the linear case
; ;

in Journal of Functional Analysis (2005), 228(1), 114-143

Schémas d'approximation associés à une équation différentielle dirigée par une fonction höldérienne; cas du mouvement brownien fractionnaire

in Comptes Rendus de l'Académie des Sciences. Série I. Mathématique (2005), 340(8), 611-614

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# 2003

Approximation at first and second order of m-order integrals of the fractional Brownian motion and of certain semimartingales
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in Electronic Journal of Probability (2003), 8(18), 1-26

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