index

Homepage of Giovanni Peccati
<giovanni.peccati(AT)gmail.com>

Born in Cremona. Full Professor, University of Paris X.

Research interests: Stochastic analysis on Wiener and other spaces; Exchangeability; Dirichlet-type processes; Limit theorems; Stein's method; Gaussian processes; Mathematical finance; Mathematical statistics; Combinatorics; Group representations; Harmonic Analysis on Groups & Homogeneous spaces ; Survival Analysis.

Groupe de Travail: "Aspects Fractals"

My Erdos Number is : 2 (can't get lower)

Articles and preprints

(1) "A representation result for time-space Brownian chaos" (2001), Annales de l'Institut H. Poincaré, 37, 607-625

(2) "On the convergence of multiple random integrals" (2001), Studia Sc. Mat. Hungarica, 37, 429-470

(3) "Explicit formulae for time-space Brownian chaos" (2003), Bernoulli, 9, 25-48

(4) "Hardy's inequality in L² and principal values of Brownian local times" (2004, with Marc Yo r), Asymptotic Methods in Stochastics, AMS, Fields Institute Communications Series, 49-74

(5) "Four limit theorems for quadratic functionals of Brownian motion and Brownian bridge" (2004, with Marc Yo r), Asymptotic Methods in Stochastics, AMS, Fields Institute Communication Series, 75-87

(6) "Hoeffding decompositions for exchangeable sequences and chaotic representation for functionals of Dirichlet processes" (2003), C.R.A.S. - Mathématiques, Vol. 336/10, 845-850

(7) "Hoeffding-ANOVA decompositions for symmetric statistics of exchangeable observations" (2004), The Annals of Probability ,32 (3A), 1796-1829

(8) "Central limit theorems for sequences of multiple stochastic integrals" (with David Nuala rt; 2005), The Annals of Probability, 33(1), 177-193

(9) "Anticipative stochastic integration based on time-space chaos" (2004), Stochastic Processes and Their Applications, 112(2), 331-355

(10) "Gaussian limits for vector-valued multiple stochastic integrals" (with Ciprian A. Tudor, 2004), Séminaire de Probabilités XXXVIII, 247-262

(11) "Weak convergence to Ocone martingales: a remark" (2004). Electronic Communications in Probability 9, 172-174

(12) "Martingale structure of Skorohod integral processes" (with Michèle Thieullen and Ciprian A. Tudor; 2006). The Annals of Probability. 34(3), 1217-1239

(13) "A time-space hedging theory" (2004). Submitted.

(14) "Multiple integral representation for functionals of Dirichlet processes" (2007). To appear in: Bernoulli

(15) "On quadratic functionals of the Brownian sheet and related processes" (with Paul Deheuv els and Marc Yor, 2006). Stochastic Processes and Their Applications 116 (3), 493-538

(16) "Identities in law between quadratic functionals of bivariate Gaussian processes, through Fubini theorems and symmetric projections" (with Marc Yor; 2006). In the volume: Approximation and Probability. Banach Center Publications n. 72, Warzawa, Poland, pp. 235-250.

(17) "Anticipating integrals and martingales on the Poisson space" (with C.A. Tudor; 2007). Random Operators and Stochastic Equations 15, 327-352.

(18) "Decompositions of stochastic processes based on irreducible group representations" (with J.-R. Pycke; 2005). Submitted.

(19) "Stable convergence of L² generalized stochastic integrals and the principle of conditioning" (with M.S. Taqqu, 2007). The Electronic Journal of Probability, paper n. 15, 447-480 (Electronic)

(20) "Limit theorems for multiple stochastic integrals" (with M.S. Taqqu, 2007). Submitted.

(21) "Central limit theorems for double Poisson integrals", (with M.S. Taqqu, 2008). To appear in : Bernoulli.

(There exists another (long) paper, by M.S. Taqqu and myself, with the title "Central limit theorems for double Poisson integrals", roughly corresponding to a less detailed presentation of the material discussed in Ref. 20 and Ref. 21. You can find it here.)

(22) "Stable convergence of multiple Wiener-Itô integrals" (with M.S. Taqqu, 2006). To appear in: The Journal of Theoretical Probability

(23) "High-frequency asymptotics for subordinated isotropic fields on an Abelian compact group" (with D. Marinucci, 2008). Stochastic Processes and their Applications 118, 585-618.

(24) "Hoeffding decompositions and urn sequences" (with O. El-Dakkak, 2006). To appear in: The Annals of Probability.

(25) "Linear and quadratic functionals of random hazard rates: an asymptotic analysis" (with I . Pruenster, 2006). To appear in: The Annals of Applied Probability.

(26) "Differentiating sigma-fields for Gaussian and shifted Gaussian processes" (with S. Darses and I. Nourdin, 2007). To appear in: Stochastics.

(27) "Burkholder's submartingales from a stochastic calculus perspective" (with M. Yor, 2007). To appear in: The Illinois Journal of Mathematics.

(28) "Group representations and high-resolution central limit theorems for subordinated spherical random fields". (with D. Marinucci, 2007). Submitted.

(29) "Gaussian Approximations of Multiple Integrals" (2007). Electronic Communications in Probability, paper n. 34, 350-364 (Electronic)

(30) "Asymptotics for posterior hazards" (with P. De Bl a si and I . Pruenster, 2007). To appear in: The Annals of Statistics.

(31) "Non-central convergence of multiple integrals" (with I. Nourdin, 2007). Under revision for: The Annals of Probability.

(32) "Weighted power variations of iterated Brownian motion" (with I. Nourdin, 2007). To appear in: The Electronic Journal of Probability.

(33) "Stein's method on Wiener chaos" (with I. Nourdin, 2007). To appear in: Probability Theory and Related Fields.

(34) "Stein's method and exact Berry-Esséen asymptotics for functionals of Gaussian fields" (with I. Nourdin, 2008). Submitted.

(35) "Multivariate normal approximations using Stein's method and Malliavin calculus" (with I. Nourdin and A. Reveillac, 2008). Submitted.

(36) "Representations of SO(3) and angular polyspectra" (with D. Marinucci, 2008). Submitted.

(37) "Stein's method and normal approximation of Poisson functionals" (with J.L. Solé, M.S. Taqqu and F. Utzet, 2008). Submitted.

Document de synthèse (En Français - A portrait of my scientific research as of September 14, 2006)

"Analyse Stochastique et Décompositions Orthogonales. Théorèmes de Convergence et de Représentation". La soutenance a eu lieu le 4 décembre 2006. Le jury était : P. Baldi, P. Deheuvels, A. Millet, N. Privault, F. Russo, M. Yor. Rapporteurs : S. Kwapien, M. Lifshits, F. Russo.

Ph. D. Thesis

Title: "Chaos Brownien d'espace-temps, décompositions de Hoeffding et problèmes de convergence associés". Supervisor: Marc Yor. Defended on December 13, 2002, at the University of Paris VI.

Forthcoming Events

Tutorial lectures on "Stein's method and infinite-dimensional Gaussian analysis". Progress in Stein's method, Singapore, January 5-9, 2009.

Invited speaker at the Workshop on Stein's method. Progress in Stein's method, Singapore, January 12-16, 2009.

Invited speaker at the Workshop on Infinitely Divisible Processes. CIMAT, Guanajuato, Mexico. March 15-21, 2009.

Invited speaker at the conference Non-semimartingales and related topics, Helsinki, Finland, May 26-28, 2009.

Invited speaker at the International conference on self-similar processes and their applications. Anger. July 20-24, 2009.

Past events

Talk: "Stein's method and stochastic analysis on Wiener chaos". Thiele Seminar, Aarhus (DK). April 24, 2008.

Exposé au Séminaire de Probabilités du LPMA (Paris VI). 13 mai 2008.

Convegno in onore del Prof. D.M. Cifarelli. Università Bocconi (Milano). 6-7 giugno 2008.

Invited speaker at the conference Journées Fractionnaires Parisiennes. Paris, 9-10 juin 2008.

Talk: "Stein's method on a Gaussian space". UAB, Barcelona. March 12, 2008.

Talk: "High-resolution asymptotics on the sphere and Clebsch-Gordan coefficients". Luxembourg University, march 18, 2008.

Invited speaker at the Workshop on Stein's Method. Singapore, March 31 - April 4, 2008.

Exposé : "La méthode de Stein sur un espace Gaussien: bornes de Berry-Esséen et développements de Edgeworth locaux", Université de Marne-la-Vallée, 11.4.2008.

Exposé: "La méthode de Stein sur un espace Gaussien". 13 février 2008, GdT Aspects Fractals (Paris VI)

Invited speaker at the conference Limit Theorems and Applications. Université Paris I, January 14-16, 2008.

Talk : "Path-dependence and stochastic processes", Boston University. October 25, 2007.

Invited talk: "High-frequency asymptotics for subordinated isotropic fields". Conference Probability and Statistics in Science and Technology. Porto, 30th Aug. / 1st Sept. 2007

Invited talk: "High-resolution asymptotics on the sphere and Clebsch-Gordan random walks". Conference Stochastic Analysis and Related Fields. Toulouse, June 20-21, 2007

Invited talk: "Stable convergence, projection and prediction: the example of fractional processes". ASMDA_2007. Crete, May 28 / June 1st, 2007.

Exposé : "Théorèmes à haute fréquence sur un espace homogène : cumulants et convolutions". LPMA, Paris VI. 27 Avril 2007.

Talk : "Stable convergence of generalized stochastic integrals, and applications to Bayesian survival analysis". Boston University, March 6, 2007

Exposé : "Convergence faible et stable des fonctionnelles des mesures aléatoires : quelques applications", Toulouse, 27 février 2007

Exposé : "Théorèmes limites pour les fonctionnelles des mesures aléatoires : une application aux champs aléatoires isotropiques". Université de Evry, 18 janvier 2007.

Exposé : "Théorèmes limites à haute fréquence pour les champs isotropiques sur les espaces homogènes". CEREMADE, 5 décembre 2006.

I visited the Department of Mathematics of Warsaw University from Monday, September 25 until Friday, September 29, 2006. I also gave a talk there on September 28, with the title "Path-dependence and chaos".

I was one of the organizers and speakers of the special session "Stochastic processes and their applications" (july 6, 2006), in the occasion of the joint SIMAI-SMAI-SMF-UMI meeting "Mathematics and Applications", held in Turin on july 3-7, 2006.

Talk : "Convergenza stabile di integrali stocastici generalizzati". Università di Roma Tor Vergata. 27 aprile 2006

Talk: "Stable convergence of multiple stochastic integrals, I: diagonal measures, cumulants and martingales". Tuesday, February 7, 2006. Boston University, Departement of Mathematics.

Talk: "Stable convergence of multiple stochastic integrals, II: decoupling, filtrations on Gaussian spaces and applications to statistics". Thursday, February 9, 2006. Boston University, Departement of Mathematics.

Talk: "Quadratic functionals of Gaussian processes and irreducible group representations". Friday, September 30, 2005. University of Technology in Helsinki. Institute of Mathematics.

Talk: "On a class of stochastic integrals related to the notion of path-dependence". Wednesday, October 5, 2005. University of Jyva¨skyla¨.

Exposé: "Convergence stable sur l'espace de Wiener". Séminaire de l'ENSAE. Jeudi, 30 juin 2005.

Exposé: "Intégration de Skorohod basèe sur la notion de dépendance trajectorielle". Matinée Calcul Stochastique, Université Paris I. Vendredi, 17 juin 2005.

Talk: "Anticipative stochastic integration based on the notion of path dependence". Joint session of the Midland Probability Seminars and of the Stochastic Analysis Seminars. University of Warwick, UK. May 25, 2005.

Invited talk: "Stable convergence on Wiener space, the principle of conditioning and martingale theory", in the occasion of the conference Analytical methods in number theory, Probability and Statistics (Linnik memorial). St. Petersbourg, Russia . April 28, 2005.

Invited Talk at the conference "Approximation and Probability" (Bedlewo, Poland. September 20-24, 2004)

Talk for the Bernoulli Conference 2004 (Barcelona, Spain. July 26-31, 2004)

Other papers

"Some results about Itô processe with jumps" (1998), Atti del XXIII Convegno AMASES

"From Wiener to time-space chaos, via conditioned Gaussian measures" (2001), Preprint n. 648 du Laboratoire de Probabilités de l'Université Paris VI

"Sui fondamenti della probabilità" (Italian; 2002), La scuola classica di Cremona, 283-292

(Something beautiful )