Representations of SO(3) and angular plyspectra (2008)
Marinucci, Domenico, Peccati, Giovanni
We characterize the angular polyspectra, of arbitrary order, associated with isotropic fields defined on the sphere S^2. Our techniques rely heavily on group representation theory, and specifically...
Stein's method on Wiener chaos (2008)
Nourdin, Ivan, Peccati, Giovanni
We combine Malliavin calculus with Stein's method, in order to derive explicit bounds in the Gaussian and Gamma approximations of random variables in a fixed Wiener chaos of a general Gaussian...
Stein's method on Wiener chaos (2008)
Nourdin, Ivan, Peccati, Giovanni
We combine Malliavin calculus with Stein's method, in order to derive explicit bounds in the Gaussian and Gamma approximations of random variables in a fixed Wiener chaos of a general Gaussian...
Multivariate normal approximation using Stein's method and Malliavin calculus (2008)
Nourdin, Ivan, Peccati, Giovanni, Réveillac, Anthony
We combine Stein's method with Malliavin calculus in order to obtain explicit bounds in the multidimensional normal approximation (in the Wasserstein distance) of functionals of Gaussian fields. Our...
Multivariate normal approximation using Stein's method and Malliavin calculus (2008)
Nourdin, Ivan, Peccati, Giovanni, Réveillac, Anthony
We combine Stein's method with Malliavin calculus in order to obtain explicit bounds in the multidimensional normal approximation (in the Wasserstein distance) of functionals of Gaussian fields. Our...
Multivariate normal approximation using Stein's method and Malliavin calculus (2008)
Nourdin, Ivan, Peccati, Giovanni, Réveillac, Anthony
We combine Stein's method with Malliavin calculus in order to obtain explicit bounds in the multidimensional normal approximation (in the Wasserstein distance) of functionals of Gaussian fields. Our...
Anticipating integrals and martingales on the Poisson space (2008)
Peccati, Giovanni, Tudor, Ciprian
Let $\tilde{N}_{t}$ be a standard compensated Poisson process on $[0,1]$. We prove a new characterization of anticipating integrals of the Skorohod type with respect to $\tilde{N}$, and use it to...
Anticipating integrals and martingales on the Poisson space (2008)
Peccati, Giovanni, Tudor, Ciprian
Let $\tilde{N}_{t}$ be a standard compensated Poisson process on $[0,1]$. We prove a new characterization of anticipating integrals of the Skorohod type with respect to $\tilde{N}$, and use it to...
Martingale structure of Skorohod integral processes (2008)
Peccati, Giovanni, Thieullen, Michèle, Tudor, Ciprian
Let the process Y(t) be a Skorohod integral process with respect to Brownian motion. We use a recent result by Tudor (2004), to prove that Y(t) can be represented as the limit of linear combinations...
Martingale structure of Skorohod integral processes (2008)
Peccati, Giovanni, Thieullen, Michèle, Tudor, Ciprian
Let the process Y(t) be a Skorohod integral process with respect to Brownian motion. We use a recent result by Tudor (2004), to prove that Y(t) can be represented as the limit of linear combinations...
Multiple integral representation for functionals of Dirichlet processes (2008)
We point out that a proper use of the Hoeffding--ANOVA decomposition for symmetric statistics of finite urn sequences, previously introduced by the author, yields a decomposition of the space of...
Stein's method and exact Berry-Esséen asymptotics for functionals of Gaussian fields (2008)
Nourdin, Ivan, Peccati, Giovanni
We show how to detect optimal Berry-Esséen bounds in the normal approximation of functionals of Gaussian fields. Our techniques are based on a combination of Malliavin calculus, Stein's method and...
Stein's method and exact Berry-Esséen asymptotics for functionals of Gaussian fields (2008)
Nourdin, Ivan, Peccati, Giovanni
We show how to detect optimal Berry-Esséen bounds in the normal approximation of functionals of Gaussian fields. Our techniques are based on a combination of Malliavin calculus, Stein's method and...
Stein's method and exact Berry-Ess\'een asymptotics for functionals of Gaussian fields (2008)
Nourdin, Ivan, Peccati, Giovanni
We show how to detect optimal Berry-Ess\'een bounds in the normal approximation of functionals of Gaussian fields. Our techniques are based on a combination of Malliavin calculus, Stein's method and...
Stein's method on Wiener chaos (2008)
Nourdin, Ivan, Peccati, Giovanni
We combine Malliavin calculus with Stein's method, in order to derive explicit bounds in the Gaussian and Gamma approximations of random variables in a fixed Wiener chaos of a general Gaussian...
Stein's method on Wiener chaos (2008)
Nourdin, Ivan, Peccati, Giovanni
We combine Malliavin calculus with Stein's method, in order to derive explicit bounds in the Gaussian and Gamma approximations of random variables in a fixed Wiener chaos of a general Gaussian...
Stein's method on Wiener chaos (2007)
Nourdin, Ivan, Peccati, Giovanni
We combine Malliavin calculus with Stein's method, in order to derive explicit bounds in the Gaussian and Gamma approximations of random variables in a fixed Wiener chaos of a general Gaussian...
Weighted power variations of iterated Brownian motion (2007)
Nourdin, Ivan, Peccati, Giovanni
We characterize the asymptotic behaviour of the weighted power variation processes associated with iterated Brownian motion. We prove weak convergence results in the sense of finite dimensional...
Weighted power variations of iterated Brownian motion (2007)
Nourdin, Ivan, Peccati, Giovanni
We characterize the asymptotic behaviour of the weighted power variation processes associated with iterated Brownian motion. We prove weak convergence results in the sense of finite dimensional...
Weighted power variations of iterated Brownian motion (2007)
Nourdin, Ivan, Peccati, Giovanni
We characterize the asymptotic behaviour of the weighted power variation processes associated with iterated Brownian motion. We prove weak convergence results in the sense of finite dimensional...
Gaussian Approximations of Multiple Integrals (2007)
Peccati, Giovanni; Université Paris VI; Giovanni.peccati@gmail.com
Fix k≥1, and let I(l), l ≥ 1, be a sequence of k-dimensional vectors of multiple Wiener-Itô integrals with respect to a general Gaussian process. We establish necessary and sufficient...
Gaussian Approximations of Multiple Integrals (2007)
Peccati, Giovanni; Université Paris VI; Giovanni.peccati@gmail.com
Fix k≥1, and let I(l), l ≥ 1, be a sequence of k-dimensional vectors of multiple Wiener-Itô integrals with respect to a general Gaussian process. We establish necessary and sufficient...
Non-central convergence of multiple integrals (2007)
Nourdin, Ivan, Peccati, Giovanni
Fix $\nu >0$, denote by $G(\nu/2)$ a Gamma random variable with parameter $\nu/2$, and let $n\geq2$ be an even integer. Consider a sequence $\{F_k\}_{k\geq 1}$ of square integrable random variables,...
Non-central convergence of multiple integrals (2007)
Nourdin, Ivan, Peccati, Giovanni
Fix $\nu >0$, denote by $G(\nu/2)$ a Gamma random variable with parameter $\nu/2$, and let $n\geq2$ be an even integer. Consider a sequence $\{F_k\}_{k\geq 1}$ of square integrable random variables,...
Non-central convergence of multiple integrals (2007)
Nourdin, Ivan, Peccati, Giovanni
Fix $\nu >0$, denote by $G(\nu/2)$ a Gamma random variable with parameter $\nu/2$, and let $n\geq2$ be an even integer. Consider a sequence $\{F_k\}_{k\geq 1}$ of square integrable random variables,...
Marinucci, Domenico, Peccati, Giovanni
We study the weak convergence (in the high-frequency limit) of the frequency components associated with Gaussian-subordinated, spherical and isotropic random fields. In particular, we provide...
Marinucci, Domenico, Peccati, Giovanni
We study the weak convergence (in the high-frequency limit) of the frequency components associated with Gaussian-subordinated, spherical and isotropic random fields. In particular, we provide...
Gaussian Approximations of Multiple Integrals (2007)
Fix an integer k, and let I(l), l=1,2,..., be a sequence of k-dimensional vectors of multiple Wiener-Itô integrals with respect to a general Gaussian process. We establish necessary and sufficient...
Gaussian Approximations of Multiple Integrals (2007)
Fix an integer k, and let I(l), l=1,2,..., be a sequence of k-dimensional vectors of multiple Wiener-It\^o integrals with respect to a general Gaussian process. We establish necessary and sufficient...
Gaussian Approximations of Multiple Integrals (2007)
Fix an integer k, and let I(l), l=1,2,..., be a sequence of k-dimensional vectors of multiple Wiener-Itô integrals with respect to a general Gaussian process. We establish necessary and sufficient...
Marinucci, Domenico, Peccati, Giovanni
We study the weak convergence (in the high-frequency limit) of the frequency components associated with Gaussian-subordinated, spherical and isotropic random fields. In particular, we provide...
Marinucci, Domenico, Peccati, Giovanni
We study the weak convergence (in the high-frequency limit) of the frequency components associated with Gaussian-subordinated, spherical and isotropic random fields. In particular, we provide...
Marinucci, Domenico, Peccati, Giovanni
We study the weak convergence (in the high-frequency limit) of the frequency components associated with Gaussian-subordinated, spherical and isotropic random fields. In particular, we provide...
Burkholder's submartingales from a stochastic calculus perspective (2007)
We provide a simple proof, as well as several generalizations, of a recent result by Davis and Suh, characterizing a class of continuous submartingales and supermartingales that can be expressed in...
Burkholder's submartingales from a stochastic calculus perspective (2007)
We provide a simple proof, as well as several generalizations, of a recent result by Davis and Suh, characterizing a class of continuous submartingales and supermartingales that can be expressed in...
Burkholder's submartingales from a stochastic calculus perspective (2007)
We provide a simple proof, as well as several generalizations, of a recent result by Davis and Suh, characterizing a class of continuous submartingales and supermartingales that can be expressed in...
Differentiating sigma-fields for Gaussian and shifted Gaussian processes (2007)
Darses, Sébastien, Nourdin, Ivan, Peccati, Giovanni
We study the notions of differentiating and non-differentiating sigma-fields in the general framework of (possibly drifted) Gaussian processes, and characterize their invariance properties under...
Differentiating sigma-fields for Gaussian and shifted Gaussian processes (2007)
Darses, Sébastien, Nourdin, Ivan, Peccati, Giovanni
We study the notions of differentiating and non-differentiating sigma-fields in the general framework of (possibly drifted) Gaussian processes, and characterize their invariance properties under...
Differentiating sigma-fields for Gaussian and shifted Gaussian processes (2007)
Darses, Sébastien, Nourdin, Ivan, Peccati, Giovanni
We study the notions of differentiating and non-differentiating sigma-fields in the general framework of (possibly drifted) Gaussian processes, and characterize their invariance properties under...
Linear and quadratic functionals of random hazard rates: an asymptotic analysis (2006)
Peccati, Giovanni, Prünster, Igor
A popular Bayesian nonparametric approach to survival analysis consists in modeling hazard rates as kernel mixtures driven by a completely random measure. In this paper we derive asymptotic results...
Linear and quadratic functionals of random hazard rates: an asymptotic analysis (2006)
Peccati, Giovanni, Prünster, Igor
A popular Bayesian nonparametric approach to survival analysis consists in modeling hazard rates as kernel mixtures driven by a completely random measure. In this paper we derive asymptotic results...
Linear and quadratic functionals of random hazard rates: an asymptotic analysis (2006)
Peccati, Giovanni, Prünster, Igor
A popular Bayesian nonparametric approach to survival analysis consists in modeling hazard rates as kernel mixtures driven by a completely random measure. In this paper we derive asymptotic results...
Linear and quadratic functionals of random hazard rates: an asymptotic analysis (2006)
Peccati, Giovanni, Prünster, Igor
A popular Bayesian nonparametric approach to survival analysis consists in modeling hazard rates as kernel mixtures driven by a completely random measure. In this paper we derive asymptotic results...
Hoeffding decompositions and two-colour urn sequences (2006)
El-Dakkak, Omar, Peccati, Giovanni
Let X be a non-deterministic infinite exchangeable sequence with values in {0,1}. We show that X is Hoeffding-decomposable if, and only if, X is either an i.i.d. sequence or a Polya sequence. This...
Hoeffding decompositions and two-colour urn sequences (2006)
El-Dakkak, Omar, Peccati, Giovanni
Let X be a non-deterministic infinite exchangeable sequence with values in {0,1}. We show that X is Hoeffding-decomposable if, and only if, X is either an i.i.d. sequence or a Polya sequence. This...
Hoeffding decompositions and two-colour urn sequences (2006)
El-Dakkak, Omar, Peccati, Giovanni
Let X be a non-deterministic infinite exchangeable sequence with values in {0,1}. We show that X is Hoeffding-decomposable if, and only if, X is either an i.i.d. sequence or a Polya sequence. This...
Hoeffding decompositions and two-colour urn sequences (2006)
El-Dakkak, Omar, Peccati, Giovanni
Let X be a non-deterministic infinite exchangeable sequence with values in {0,1}. We show that X is Hoeffding-decomposable if, and only if, X is either an i.i.d. sequence or a Polya sequence. This...
Hoeffding decompositions and two-colour urn sequences (2006)
El-Dakkak, Omar, Peccati, Giovanni
Let X be a non-deterministic infinite exchangeable sequence with values in {0,1}. We show that X is Hoeffding-decomposable if, and only if, X is either an i.i.d. sequence or a Polya sequence. This...
High-frequency asymptotics for subordinated isotropic fields on an Abelian compact group (2006)
Marinucci, Domenico, Peccati, Giovanni
Let T* be a random field indexed by an Abelian compact group G, and suppose that T* has the form T* = F(T(g)), where T is Gaussian and isotropic. The aim of this paper is to establish high-frequency...
High-frequency asymptotics for subordinated isotropic fields on an Abelian compact group (2006)
Marinucci, Domenico, Peccati, Giovanni
Let T* be a random field indexed by an Abelian compact group G, and suppose that T* has the form T* = F(T(g)), where T is Gaussian and isotropic. The aim of this paper is to establish high-frequency...
High-frequency asymptotics for subordinated isotropic fields on an Abelian compact group (2006)
Marinucci, Domenico, Peccati, Giovanni
Let T* be a random field indexed by an Abelian compact group G, and suppose that T* has the form T* = F(T(g)), where T is Gaussian and isotropic. The aim of this paper is to establish high-frequency...
High-frequency asymptotics for subordinated isotropic fields on an Abelian compact group (2006)
Marinucci, Domenico, Peccati, Giovanni
Let T* be a random field indexed by an Abelian compact group G, and suppose that T* has the form T* = F(T(g)), where T is Gaussian and isotropic. The aim of this paper is to establish high-frequency...
High-frequency asymptotics for subordinated isotropic fields on an Abelian compact group (2006)
Marinucci, Domenico, Peccati, Giovanni
Let T* be a random field indexed by an Abelian compact group G, and suppose that T* has the form T* = F(T(g)), where T is Gaussian and isotropic. The aim of this paper is to establish high-frequency...
Martingale structure of Skorohod integral processes (2006)
Peccati, Giovanni, Thieullen, Michèle, Tudor, Ciprian A.
Let the process {Yt,t∈[0,1]} have the form Yt=δ(u1[0,t]), where δ stands for a Skorohod integral with respect to Brownian motion and u is a measurable process that verifies some suitable...
Peccati, Giovanni, Taqqu, Murad
Consider generalized adapted stochastic integrals with respect to independently scattered random measures with second moments. We use a decoupling technique, known as the "principle of conditioning"...
Stable convergence of multiple Wiener-Itô integrals (2006)
Peccati, Giovanni, Taqqu, Murad
We prove sufficient conditions, ensuring that a sequence of multiple Wiener-Itô integrals (with respect to a general Gaussian process) converges stably to a mixture of normal distributions. Our key...
Stable convergence of multiple Wiener-Itô integrals (2006)
Peccati, Giovanni, Taqqu, Murad
We prove sufficient conditions, ensuring that a sequence of multiple Wiener-Itô integrals (with respect to a general Gaussian process) converges stably to a mixture of normal distributions. Our key...
Peccati, Giovanni, Taqqu, Murad
Consider generalized adapted stochastic integrals with respect to independently scattered random measures with second moments. We use a decoupling technique, known as the "principle of conditioning"...
Stable convergence of multiple Wiener-Itô integrals (2006)
Peccati, Giovanni, Taqqu, Murad
We prove sufficient conditions, ensuring that a sequence of multiple Wiener-Itô integrals (with respect to a general Gaussian process) converges stably to a mixture of normal distributions. Our key...
Peccati, Giovanni, Taqqu, Murad
Consider generalized adapted stochastic integrals with respect to independently scattered random measures with second moments. We use a decoupling technique, known as the "principle of conditioning"...
Peccati, Giovanni, Taqqu, Murad S.
Consider generalized adapted stochastic integrals with respect to independently scattered random measures with second moments. We use a decoupling technique, known as the "principle of conditioning",...
Stable convergence of multiple Wiener-It\^{o} integrals (2006)
Peccati, Giovanni, Taqqu, Murad S.
We prove sufficient conditions, ensuring that a sequence of multiple Wiener-It\^{o} integrals (with respect to a general Gaussian process) converges stably to a mixture of normal distributions. Our...
Stable convergence of multiple Wiener-Itô integrals (2006)
Peccati, Giovanni, Taqqu, Murad
We prove sufficient conditions, ensuring that a sequence of multiple Wiener-Itô integrals (with respect to a general Gaussian process) converges stably to a mixture of normal distributions. Our key...
Peccati, Giovanni, Taqqu, Murad
Consider generalized adapted stochastic integrals with respect to independently scattered random measures with second moments. We use a decoupling technique, known as the "principle of conditioning"...
Decompositions of stochastic processes based on irreducible group representations (2005)
Peccati, Giovanni, Pycke, Jean-Renaud
Let G be a topological compact group acting on some space Y. We study a decomposition of Y-indexed stochastic processes, based on the orthogonality relations between the characters of the irreducible...
Decompositions of stochastic processes based on irreducible group representations (2005)
Peccati, Giovanni, Pycke, Jean-Renaud
Let G be a topological compact group acting on some space Y. We study a decomposition of Y-indexed stochastic processes, based on the orthogonality relations between the characters of the irreducible...
Decompositions of stochastic processes based on irreducible group representations (2005)
Peccati, Giovanni, Pycke, Jean-Renaud
Let G be a topological compact group acting on some space Y. We study a decomposition of Y-indexed stochastic processes, based on the orthogonality relations between the characters of the irreducible...
Decompositions of stochastic processes based on irreducible group representations (2005)
Peccati, Giovanni, Pycke, Jean-Renaud
Let G be a topological compact group acting on some space Y. We study a decomposition of Y-indexed stochastic processes, based on the orthogonality relations between the characters of the irreducible...
Decompositions of stochastic processes based on irreductible group representations (2005)
Peccati, Giovanni, Pycke, Jean-Renaud
Let G be a topological compact group acting on some space Y. We study a decomposition of Y-indexed stochastic processes, based on the orthogonality relations between the characters of the irreducible...
Anticipating integrals and martingales on the Poisson space (2005)
Peccati, Giovanni, Tudor, Ciprian
Let $\tilde{N}_{t}$ be a standard compensated Poisson process on $[0,1]$. We prove a new characterization of anticipating integrals of the Skorohod type with respect to $\tilde{N}$, and use it to...
Anticipating integrals and martingales on the Poisson space (2005)
Peccati, Giovanni, Tudor, Ciprian
Let $\tilde{N}_{t}$ be a standard compensated Poisson process on $[0,1]$. We prove a new characterization of anticipating integrals of the Skorohod type with respect to $\tilde{N}$, and use it to...
Anticipating integrals and martingales on the Poisson space (2005)
Peccati, Giovanni, Tudor, Ciprian A.
Let $\tilde{N}\_{t}$ be a standard compensated Poisson process on $[0,1]$. We prove a new characterization of anticipating integrals of the Skorohod type with respect to $\tilde{N}$, and use it to...
Central limit theorems for sequences of multiple stochastic integrals (2005)
Nualart, David, Peccati, Giovanni
We characterize the convergence in distribution to a standard normal law for a sequence of multiple stochastic integrals of a fixed order with variance converging to 1. Some applications are given,...
Martingale structure of Skorohod integral processes (2005)
Peccati, Giovanni, Thieullen, Michèle, Tudor, Ciprian
Let the process Y(t) be a Skorohod integral process with respect to Brownian motion. We use a recent result by Tudor (2004), to prove that Y(t) can be represented as the limit of linear combinations...
Martingale structure of Skorohod integral processes (2005)
Peccati, Giovanni, Thieullen, Michèle, Tudor, Ciprian
Let the process Y(t) be a Skorohod integral process with respect to Brownian motion. We use a recent result by Tudor (2004), to prove that Y(t) can be represented as the limit of linear combinations...
Martingale structure of Skorohod integral processes (2005)
Peccati, Giovanni, Thieullen, Michèle, Tudor, Ciprian A.
Let the process Y(t) be a Skorohod integral process with respect to Brownian motion. We use a recent result by Tudor (2004), to prove that Y(t) can be represented as the limit of linear combinations...
We present three new identities in law for quadratic functionals of conditioned bivariate Gaussian processes. In particular, our results provide a two-parameter generalization of a celebrated...
We present three new identities in law for quadratic functionals of conditioned bivariate Gaussian processes. In particular, our results provide a two-parameter generalization of a celebrated...
We present three new identities in law for quadratic functionals of conditioned bivariate Gaussian processes. In particular, our results provide a two-parameter generalization of a celebrated...
We present three new identities in law for quadratic functionals of conditioned bivariate Gaussian processes. In particular, our results provide a two-parameter generalization of a celebrated...
We present three new identities in law for quadratic functionals of conditioned bivariate Gaussian processes. In particular, our results provide a two-parameter generalization of a celebrated...
Central limit theorems for sequences of multiple stochastic integrals (2005)
Nualart, David, Peccati, Giovanni
We characterize the convergence in distribution to a standard normal law for a sequence of multiple stochastic integrals of a fixed order with variance converging to 1. Some applications are given,...
Weak Convergence to Ocone Martingales: a Remark (2004)
Peccati, Giovanni; Universite Pierre Et Marie Curie, France; Giovanni.peccati@libero.it
We show, by a simple counterexample, that the main result in a recent paper by H. Van Zanten [Electronic Communications in Probability 7 (2002), 215-222] is false. We eventually point out the origin...
Hoeffding-ANOVA decompositions for symmetric statistics of exchangeable observations (2004)
Consider a (possibly infinite) exchangeable sequence X={X_n:1\leqn0, X_n^{(\alpha, c)} consists of the first n instants of a generalized P\'olya urn sequence.
Hoeffding-ANOVA decompositions for symmetric statistics of exchangeable observations (2004)
Consider a (possibly infinite) exchangeable sequence X={Xn:1≤n0, Xn(α,c) consists of the first n instants of a generalized Pólya urn sequence. For every choice of α(⋅) and c, the...
Universites de Paris 6 Paris 7 - CNRS (UMR 7599) (2004)
De Probabilit, P. Deheuvels, G. Peccati, M. Yor, Paul Deheuvels, Giovanni Peccati, ...
Motivated by asymptotic problems in the theory of empirical processes, and specifically by tests of independence, we study the law of quadratic functionals of the (weighted) Brownian sheet and of the...
Universites de Paris 6 Paris 7 - CNRS (UMR 7599) PR (2004)
De Probabilit, Giovanni Peccati, Ciprian A. Tudor
We establish necessary and su#cient conditions for a sequence of d-dimensional vectors of multiple stochastic integrals F 1, to converge in distribution to a d-dimensional Gaussian vector Nd = (N1 ,...
Explicit formulae for time-space Brownian chaos (2003)
Let $F$ be a square-integrable and infinitely weakly differentiable functional of a standard Brownian motion $X$: we show that the $n$th integrand in the time-space chaotic decomposition of $F$ has...