Contributions à l'étude des processus gaussiens (2008)
Le chapitre 1 est principalement consacré au comportement asymptotique des variations à poids du mouvement brownien fractionnaire. Tout d'abord, après avoir motivé l'intérêt d'une telle étude...
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...
Nourdin, Ivan, Réveillac, Anthony
We derive the asymptotic behavior of weighted quadratic variations of fractional Brownian motion $B$ with Hurst index H=1/4. This completes the only missing case in a very recent work by I. Nourdin,...
Nourdin, Ivan, Réveillac, Anthony
We derive the asymptotic behavior of weighted quadratic variations of fractional Brownian motion $B$ with Hurst index H=1/4. This completes the only missing case in a very recent work by I. Nourdin,...
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...
Breton, Jean-Christophe, Nourdin, Ivan
Let $q\geq 2$ be a positive integer, $B$ be a fractional Brownian motion with Hurst index $H\in(0,1)$, $Z$ be an Hermite random variable of index $q$, and $H_q$ denote the Hermite polynomial having...
Breton, Jean-Christophe, Nourdin, Ivan
Let $q\geq 2$ be a positive integer, $B$ be a fractional Brownian motion with Hurst index $H\in(0,1)$, $Z$ be an Hermite random variable of index $q$, and $H_q$ denote the Hermite polynomial having...
Breton, Jean-Christophe, Nourdin, Ivan
Let $q\geq 2$ be a positive integer, $B$ be a fractional Brownian motion with Hurst index $H\in(0,1)$, $Z$ be an Hermite random variable of index $q$, and $H_q$ denote the Hermite polynomial having...
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...
Stochastic volatility: approximation and goodness-of-fit test (2008)
Gradinaru, Mihai, Nourdin, Ivan
Let $X$ be the unique solution started from $x_0$ of the stochastic differential equation $dX_t=\theta(t,X_t)dB_t+b(t,X_t)dt$, with $B$ a standard Brownian motion. We consider an approximation of the...
Stochastic volatility: approximation and goodness-of-fit test (2008)
Gradinaru, Mihai, Nourdin, Ivan
Let $X$ be the unique solution started from $x_0$ of the stochastic differential equation $dX_t=\theta(t,X_t)dB_t+b(t,X_t)dt$, with $B$ a standard Brownian motion. We consider an approximation of the...
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...
Nourdin, Ivan, Réveillac, Anthony
We derive the asymptotic behavior of weighted quadratic variations of fractional Brownian motion $B$ with Hurst index H=1/4. This completes the only missing case in a very recent work by I. Nourdin,...
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...
Central limit theorems for multiple Skorohod integrals (2008)
In this paper, we prove a central limit theorem for a sequence of iterated Shorohod integrals using the techniques of Malliavin calculus. The convergence is stable, and the limit is a conditionally...
Central limit theorems for multiple Skorohod integrals (2008)
In this paper, we prove a central limit theorem for a sequence of iterated Shorohod integrals using the techniques of Malliavin calculus. The convergence is stable, and the limit is a conditionally...
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...
Delay equations driven by rough paths (2007)
Neuenkirch, Andreas, Nourdin, Ivan, Tindel, Samy
In this article, we illustrate the flexibility of the algebraic integration formalism introduced by M. Gubinelli (2004), by establishing an existence and uniqueness result for delay equations driven...
Delay equations driven by rough paths (2007)
Neuenkirch, Andreas, Nourdin, Ivan, Tindel, Samy
In this article, we illustrate the flexibility of the algebraic integration formalism introduced by M. Gubinelli (2004), by establishing an existence and uniqueness result for delay equations driven...
Delay equations driven by rough paths (2007)
Neuenkirch, Andreas, Nourdin, Ivan, Tindel, Samy
In this article, we illustrate the flexibility of the algebraic integration formalism introduced by M. Gubinelli (2004), by establishing an existence and uniqueness result for delay equations driven...
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...
Nourdin, Ivan, Nualart, David, Tudor, Ciprian
In this paper, we prove some central and non-central limit theorems for renormalized weighted power variations of order q>1 of the fractional Brownian motion with Hurst parameter H in (0,1), where q...
Nourdin, Ivan, Nualart, David, Tudor, Ciprian
In this paper, we prove some central and non-central limit theorems for renormalized weighted power variations of order q>1 of the fractional Brownian motion with Hurst parameter H in (0,1), where q...
Dynamical properties and characterization of gradient drift diffusions (2007)
Darses, Sébastien; Boston University; Darses@math.bu.edu, Nourdin, Ivan; University Paris VI; Nourdin@ccr.jussieu.fr
We study the dynamical properties of the Brownian diffusions having σ Id as diffusion coefficient matrix and b=∇U as drift vector. We characterize this class through the equality...
Gradinaru, Mihai, Nourdin, Ivan
The first part of the paper contains the study of the convergence for some weighted power variations of a fractional Brownian motion $B$ with Hurst index $H\in(0,1)$. The behaviour is different when...
In this paper, we will focus - in dimension one - on the SDEs of the type dX_t=s(X_t)dB_t+b(X_t)dt where B is a fractional Brownian motion. Our principal motivation is to describe one of the simplest...
Gradinaru, Mihai, Nourdin, Ivan
The first part of the paper contains the study of the convergence for some weighted power variations of a fractional Brownian motion $B$ with Hurst index $H\in(0,1)$. The behaviour is different when...
In this paper, we will focus - in dimension one - on the SDEs of the type dX_t=s(X_t)dB_t+b(X_t)dt where B is a fractional Brownian motion. Our principal motivation is to describe one of the simplest...
Some linear fractional stochastic equations (2007)
Using the multiple stochastic integrals we prove an existence and uniqueness result for a linear stochastic equation driven by the fractional Brownian motion with any Hurst parameter. We study both...
Some linear fractional stochastic equations (2007)
Using the multiple stochastic integrals we prove an existence and uniqueness result for a linear stochastic equation driven by the fractional Brownian motion with any Hurst parameter. We study both...
Asymptotic expansions at any time for fractional scalar SDEs of Hurst index H>1/2 (2007)
Darses, Sébastien, Nourdin, Ivan
We study the asymptotic developments with respect to $h$ of E[D_h f(X_t)], E[D_h f(X_t)|F_t] and E[D_h f(X_t)|X_t], where D_h f(X_t)=f(X_{t+h})-f(X_t), when f:R->R is a smooth real function, t is a...
Asymptotic expansions at any time for fractional scalar SDEs of Hurst index H>1/2 (2007)
Darses, Sébastien, Nourdin, Ivan
We study the asymptotic developments with respect to $h$ of E[D_h f(X_t)], E[D_h f(X_t)|F_t] and E[D_h f(X_t)|X_t], where D_h f(X_t)=f(X_{t+h})-f(X_t), when f:R->R is a smooth real function, t is a...
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,...
Convergence in law for certain weighted quadratic variations of fractional Brownian motion (2007)
By means of Malliavin calculus, we prove the convergence in law for certain weighted quadratic variations of a fractional Brownian motion B with Hurst index H between 1/4 and 1/2.
Weak approximation of a fractional SDE (2007)
In this note, a diffusion approximation result is shown for stochastic differential equations driven by a fractional Brownian motion B with Hurst parameter H>1/3. We shall use a Gaussian regular...
Weak approximation of a fractional SDE (2007)
In this note, a diffusion approximation result is shown for stochastic differential equations driven by a fractional Brownian motion B with Hurst parameter H>1/3. We shall use a Gaussian regular...
Weak approximation of a fractional SDE (2007)
In this note, a diffusion approximation result is shown for stochastic differential equations driven by a fractional Brownian motion B with Hurst parameter H>1/3. We shall use a Gaussian regular...
Convergence in law for certain weighted quadratic variations of fractional Brownian motion (2007)
By means of Malliavin calculus, we prove the convergence in law for certain weighted quadratic variations of a fractional Brownian motion B with Hurst index H between 1/4 and 1/2.
Central limit theorems for multiple Skorohod integrals (2007)
In this paper, we prove a central limit theorem for a sequence of iterated Shorohod integrals using the techniques of Malliavin calculus. The convergence is stable, and the limit is a conditionally...
This note is devoted to a fine study of the convergence of some weighted quadratic and cubic variations of a fractional Brownian motion B with Hurst index H in (0,1/2). With the help of Malliavin...
This note is devoted to a fine study of the convergence of some weighted quadratic and cubic variations of a fractional Brownian motion B with Hurst index H in (0,1/2). With the help of Malliavin...
This note is devoted to a fine study of the convergence of some weighted quadratic and cubic variations of a fractional Brownian motion B with Hurst index H in (0,1/2). With the help of Malliavin...
Gradinaru, Mihai, Nourdin, Ivan, Russo, Francesco, Vallois, Pierre
Given an integer m, a probability measure ν on [0,1], a process X and a real function g, we define the m-order ν-integral having as integrator X and as integrand g(X). In the case of the...
This note is devoted to a fine study of the convergence of some weighted quadratic and cubic variations of a fractional Brownian motion B with Hurst index H in (0,1/2). With the help of Malliavin...
This note is devoted to a fine study of the convergence of some weighted quadratic and cubic variations of a fractional Brownian motion B with Hurst index H in (0,1/2). With the help of Malliavin...
Gradinaru, Mihai, Nourdin, Ivan, Russo, Francesco, Vallois, Pierre
Given an integer m, a probability measure ν on [0,1], a process X and a real function g, we define the m-order ν-integral having as integrator X and as integrand g(X). In the case of the...
Convergence of weighted power variations of fractional Brownian motion (2007)
Gradinaru, Mihai, Nourdin, Ivan
The first part of the paper contains the study of the convergence for some weighted power variations of a fractional Brownian motion B with Hurst index H in (0,1). The behaviour is different when...
Asymptotic developments at any time for fractional SDEs of Hurst index H>1/2 (2007)
Darses, Sébastien, Nourdin, Ivan
We study the asymptotic developments with respect to $h$ of E[D_h f(X_t)], E[D_h f(X_t)|F_t] and E[D_h f(X_t)|X_t], where D_h f(X_t)=f(X_{t+h})-f(X_t), when f:R->R is a smooth real function, t is a...
Asymptotic expansions at any time for fractional scalar SDEs of Hurst index H>1/2 (2007)
Darses, Sébastien, Nourdin, Ivan
We study the asymptotic developments with respect to $h$ of E[D_h f(X_t)], E[D_h f(X_t)|F_t] and E[D_h f(X_t)|X_t], where D_h f(X_t)=f(X_{t+h})-f(X_t), when f:R->R is a smooth real function, t is a...
Gradinaru, Mihai, Nourdin, Ivan
The first part of the paper contains the study of the convergence for some weighted power variations of a fractional Brownian motion $B$ with Hurst index $H\in(0,1)$. The behaviour is different when...
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...
Dynamical properties and characterization of gradient drift diffusions (2006)
Darses, Sébastien, Nourdin, Ivan
We study the dynamical properties of the Brownian diffusions having $\sigma\,{\rm Id}$ as diffusion coefficient matrix and $b=\nabla U$ as drift vector. We characterize this class through the...
Dynamical properties and characterization of gradient drift diffusions (2006)
Darses, Sébastien, Nourdin, Ivan
We study the dynamical properties of the Brownian diffusions having $\sigma {\rm Id}$ as diffusion coefficient matrix and $b=\nabla U$ as drift vector. We characterize this class through the equality...
Dynamical properties and characterization of gradient drift diffusions (2006)
Darses, Sébastien, Nourdin, Ivan
We study the dynamical properties of the Brownian diffusions having $\sigma\,{\rm Id}$ as diffusion coefficient matrix and $b=\nabla U$ as drift vector. We characterize this class through the...
Neuenkirch, Andreas, Nourdin, Ivan
In this paper, we derive the exact rate of convergence of some approximation schemes associated to scalar stochastic differential equations driven by a fractional Brownian motion with Hurst index H.
Neuenkirch, Andreas, Nourdin, Ivan
In this paper, we derive the exact rate of convergence of some approximation schemes associated to scalar stochastic differential equations driven by a fractional Brownian motion with Hurst index H.
Stochastic derivatives for fractional diffusions (2006)
Darses, Sébastien, Nourdin, Ivan
In this paper, we introduce some fundamental notions related to the so-called stochastic derivatives with respect to a given sigma-field Q. In our framework, we recall well known results about Markov...
Stochastic derivatives for fractional diffusions (2006)
Darses, Sébastien, Nourdin, Ivan
In this paper, we introduce some fundamental notions related to the so-called stochastic derivatives with respect to a given sigma-field Q. In our framework, we recall well known results about Markov...
Trees and asymptotic developments for fractional stochastic differential equations (2006)
Neuenkirch, Andreas, Nourdin, Ivan, Roessler, Andreas, Tindel, Samy
In this paper we consider a n-dimensional stochastic differential equation driven by a fractional Brownian motion with Hurst parameter H>1/3. After solving this equation in a rather elementary way,...
Trees and asymptotic developments for fractional stochastic differential equations (2006)
Neuenkirch, Andreas, Nourdin, Ivan, Roessler, Andreas, Tindel, Samy
In this paper we consider a n-dimensional stochastic differential equation driven by a fractional Brownian motion with Hurst parameter H>1/3. After solving this equation in a rather elementary way,...
Trees and asymptotic developments for fractional stochastic differential equations (2006)
Neuenkirch, Andreas, Nourdin, Ivan, Roessler, Andreas, Tindel, Samy
In this paper we consider a n-dimensional stochastic differential equation driven by a fractional Brownian motion with Hurst parameter H>1/3. After solving this equation in a rather elementary way,...
Gradinaru, Mihai, Nourdin, Ivan
Let X be the fractional Brownian motion of any Hurst index H in (0,1) (resp. a semimartingale) and set alpha=H (resp. alpha=1/2). If Y is a continuous process and if m is a positive integer, we study...
Gradinaru, Mihai, Nourdin, Ivan
Let X be the fractional Brownian motion of any Hurst index H in (0,1) (resp. a semimartingale) and set alpha=H (resp. alpha=1/2). If Y is a continuous process and if m is a positive integer, we study...
Ito's- and Tanaka's-type formulae for the stochastic heat equation: The linear case (2006)
Gradinaru, Mihai, Nourdin, Ivan, Tindel, Samy
In this paper, we consider the linear stochastic heat equation with additive noise in dimension one. Then, using the representation of its solution X as a stochastic convolution of the cylindrical...
Ito's- and Tanaka's-type formulae for the stochastic heat equation: The linear case (2006)
Gradinaru, Mihai, Nourdin, Ivan, Tindel, Samy
In this paper, we consider the linear stochastic heat equation with additive noise in dimension one. Then, using the representation of its solution X as a stochastic convolution of the cylindrical...
On the absolute continuity of L\'{e}vy processes with drift (2006)
We consider the problem of absolute continuity for the one-dimensional SDE \[X_t=x+\int_0^ta(X_s) ds+Z_t,\] where $Z$ is a real L\'{e}vy process without Brownian part and $a$ a function of class...
Optimal control for rough differential equations (2006)
Mazliak, Laurent, Nourdin, Ivan
In this note, we consider an optimal control problem associated to a differential equation driven by a Hölder continuous function g of index greater than 1/2. We split our study in two cases. If the...
Optimal control for rough differential equations (2006)
Mazliak, Laurent, Nourdin, Ivan
In this note, we consider an optimal control problem associated to a differential equation driven by a Hölder continuous function g of index greater than 1/2. We split our study in two cases. If the...
Optimal control for rough differential equations (2006)
Mazliak, Laurent, Nourdin, Ivan
In this note, we consider an optimal control problem associated to a differential equation driven by a Hölder continuous function g of index greater than 1/2. We split our study in two cases. If the...
Optimal control for rough differential equations (2006)
Mazliak, Laurent, Nourdin, Ivan
In this note, we consider an optimal control problem associated to a differential equation driven by a H\"{o}lder continuous function g of index greater than 1/2. We split our study in two cases. If...
Optimal control for rough differential equations (2006)
Mazliak, Laurent, Nourdin, Ivan
In this note, we consider an optimal control problem associated to a differential equation driven by a Hölder continuous function g of index greater than 1/2. We split our study in two cases. If the...
On the absolute continuity of Lévy processes with drift (2006)
We consider the problem of absolute continuity for the one-dimensional SDE Xt=x+∫0ta(Xs) ds+Zt, where Z is a real Lévy process without Brownian part and a a function of class $\mathcal{C}^{1}$...
Stochastic derivatives for fractional diffusions (2006)
Darses, Sébastien, Nourdin, Ivan
In this paper, we introduce some fundamental notions related to the so-called stochastic derivatives with respect to a given sigma-field Q. In our framework, we recall well known results about Markov...
Stochastic derivatives for fractional diffusions (2006)
Darses, Sébastien, Nourdin, Ivan
In this paper, we introduce some fundamental notions related to the so-called stochastic derivatives with respect to a given sigma-field Q. In our framework, we recall well known results about Markov...
Stochastic derivatives for fractional diffusions (2006)
Darses, Sébastien, Nourdin, Ivan
In this paper, we introduce some fundamental notions related to the so-called stochastic derivatives with respect to a given sigma-field Q. In our framework, we recall well known results about Markov...
Stochastic derivatives for fractional diffusions (2006)
Darses, Sébastien, Nourdin, Ivan
In this paper, we introduce some fundamental notions related to the so-called stochastic derivatives with respect to a given sigma-field Q. In our framework, we recall well known results about Markov...
Stochastic derivatives for fractional diffusions (2006)
Darses, Sébastien, Nourdin, Ivan
In this paper, we introduce some fundamental notions related to the so-called stochastic derivatives with respect to a given $\sigma$-field $\mathcal{Q}$. In our framework, we recall well-known...