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...
Integral representation of renormalized self-intersection local times (2008)
Hu, Yaozhong, Nualart, David, Song, Jian
In this paper we apply Clark-Ocone formula to deduce an explicit integral representation for the renormalized self-intersection local time of the $d$% -dimensional fractional Brownian motion with...
A decomposition of the bifractional Brownian motion and some applications (2008)
In this paper we show a decomposition of the bifractional Brownian motion with parameters H,K into the sum of a fractional Brownian motion with Hurst parameter HK plus a stochastic process with...
We prove an existence and uniqueness theorem for solutions of multidimensional, time dependent, stochastic differential equations driven simultaneously by a multidimensional fractional Brownian...
Occupation densities for certain processes related to fractional Brownian motion (2008)
Es-Sebaiy, Khalifa, Nualart, David, Ouknine, Youssef, Tudor, Ciprian
In this paper we establish the existence of a square integrable occupation density for two classes of stochastic processes. First we consider a Gaussian process with an absolutely continuous random...
Occupation densities for certain processes related to fractional Brownian motion (2008)
Es-Sebaiy, Khalifa, Nualart, David, Ouknine, Youssef, Tudor, Ciprian
In this paper we establish the existence of a square integrable occupation density for two classes of stochastic processes. First we consider a Gaussian process with an absolutely continuous random...
Occupation densities for certain processes related to fractional Brownian motion (2008)
Es-Sebaiy, Khalifa, Nualart, David, Ouknine, Youssef, Tudor, Ciprian
In this paper we establish the existence of a square integrable occupation density for two classes of stochastic processes. First we consider a Gaussian process with an absolutely continuous random...
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...
A singular stochastic differential equation driven by fractional Brownian motion (2007)
Hu, Yaozhong, Nualart, David, Song, Xiaoming
In this paper we study a singular stochastic differential equation driven by an additive fractional Brownian motion with Hurst parameter $H>\frac 12$. Under some assumptions on the drift, we show...
Fractional martingales and characterization of the fractional Brownian motion (2007)
Hu, Yaozhong, Nualart, David, Song, Jian
In this paper we introduce the notion of $\alpha$-martingale as the fractional derivative of order $\alpha$ of a continuous local martingale, where $ \alpha\in (-\frac 12, \frac 12)$, and we show...
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...
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.
Regularity of the density for the stochastic heat equation (2007)
We study the smoothness of the density of a semilinear heat equation with multiplicative spacetime white noise. Using Malliavin calculus, we reduce the problem to a question of negative moments of...
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...
Stochastic Heat Equation Driven by Fractional Noise and Local Time (2007)
The aim of this paper is to study the $d$-dimensional stochastic heat equation with a multiplicative Gaussian noise which is white in space and it has the covariance of a fractional Brownian motion...
Intersection local time for two independent fractional Brownian motions (2007)
Nualart, David, Ortiz-Latorre, Salvador
We prove the existence of the intersection local time for two independent, d -dimensional fractional Brownian motions with the same Hurst parameter H. Assume d greater or equal to 2, then the...
Central limit theorems for multiple stochastic integrals and Malliavin calculus (2007)
Nualart, David, Ortiz, Salvador
We give a new characterization for the convergence in distribution to a standard normal law of a sequence of multiple stochastic integrals of a fixed order with variance one, in terms of the...
Existence and smoothness of the density for spatially homogeneous SPDEs (2007)
Nualart, David, Quer-Sardanyons, Lluis
In this paper, we extend Walsh's stochastic integral with respect to a Gaussian noise, white in time and with some homogeneous spatial correlation, in order to be able to integrate some random...
Power variation of some integral fractional processes (2006)
Manuel Corcuera, José, Nualart, David, Woerner, Jeannette H. C.
We consider the asymptotic behaviour of the realized power variation of processes of the form . We establish the stable convergence of the corresponding fluctuations. These results provide new...
Hitting times for Gaussian processes (2006)
Decreusefond, Laurent, Nualart, David
We establish a general formula for the Laplace transform of the hitting times of a Gaussian process. Some consequences are derived, and particular cases like the fractional Brownian motion are...
Notes on the two-dimensional fractional Brownian motion (2006)
Baudoin, Fabrice, Nualart, David
We study the two-dimensional fractional Brownian motion with Hurst parameter $H>{1/2}$. In particular, we show, using stochastic calculus, that this process admits a skew-product decomposition and...
Rough Path Analysis Via Fractional Calculus (2006)
Using fractional calculus we define integrals of the form $% \int_{a}^{b}f(x_{t})dy_{t}$, where $x$ and $y$ are vector-valued H\"{o}lder continuous functions of order $\displaystyle \beta \in...
Notes on the two-dimensional fractional Brownian motion (2006)
Baudoin, Fabrice, Nualart, David
We study the two-dimensional fractional Brownian motion with Hurst parameter H>½. In particular, we show, using stochastic calculus, that this process admits a skew-product decomposition and deduce...
Renormalized self-intersection local time for fractional Brownian motion (2005)
Let B_t^H be a d-dimensional fractional Brownian motion with Hurst parameter H\in(0,1). Assume d\geq2. We prove that the renormalized self-intersection local...
Renormalized self-intersection local time for fractional Brownian motion (2005)
Let BtH be a d-dimensional fractional Brownian motion with Hurst parameter H∈(0,1). Assume d≥2. We prove that the renormalized self-intersection local time...
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,...
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,...
Some Processes Associated with Fractional Bessel Processes (2004)
Let $B=\{(B_{t}^{1},..., B_{t}^{d}), t\geq 0\}$ be a $d$-dimensional fractional Brownian motion with Hurst parameter $H$ and let $R_{t}=% \sqrt{(B_{t}^{1})^{2}+... +(B_{t}^{d})^{2}}$ be the...
Probabilistic models for vortex filaments based on fractional Brownian motion (2003)
Nualart, David, Rovira, Carles, Tindel, Samy
We consider a vortex structure based on a three-dimensional fractional Brownian motion with Hurst parameter $H>\frac{1}{2}.$ We show that the energy $\mathbb{H}$\vspace*{-1pt} has moments of any...
Smoothness of the law of the supremum of the fractional Brownian motion (2003)
Zaïdi, Noureddine Lanjri; Université Ibn Tofaïl, Kénitra, Maroc; Nour@mixmail.com, Nualart, David; Universitat De Barcelona; Nualart@mat.ub.es
This note is devoted to prove that the supremum of a fractional Brownian motion with Hurst parameter $Hin left( 0,1right)$ has an infinitely differentiable density on $left( 0,infty right)$. The...
Additional Utility of Insiders with Imperfect Dynamical Information (2003)
Corcuera, José Mª, Peter Imkeller, Kohatsu-Higa, Arturo, Nualart, David
In this paper we consider an insider with privileged information that is affected by an independent noise vanishing as the revelation time approaches. At this time, information is available to every...
Nualart, David, Schoutens, Wim
In this paper we show the existence and uniqueness of a solution for backward stochastic differential equations driven by a Lévy process with moments of all orders. The results are important from a...
Stochastic Calculus with Respect to Gaussian Processes (2001)
Mazet, Olivier, Nualart, David
In this paper we develop a stochastic calculus with respect to a Gaussian process of the form $B_t = \int^t_0 K(t, s)\, dW_s$, where $W$ is a Wiener process and $K(t, s)$ is a square integrable...
Prepublications du Departement de Mathematiques (2001)
La Rochelle Cedex, Laure Coutin, David Nualart, Facultat De Matematiques, Ciprian A. Tudor
this paper is to establish the following version of Tanaka's formula for the fractional Brownian motion, assuming H > t : (2) The stochastic integral appearing in this formula coincides the...
BSDE's, Clark-Ocone Formula, and Feynman-Kac Formula for L'evy Processes (2000)
David Nualart, Gran Via, Corts Catalanes, Wim Schoutens
In this paper we show the existence and uniqueness of a solution for backward stochastic differential equations driven by a L'evy process with moments of all orders. An application to Clark-Ocone and...
Brownian Motion Reflected On Brownian Motion (2000)
Krzysztof Burdzy, David Nualart
Introduction. We will investigate some aspects of the local time, parabolic measure and excursion theory of Brownian motion reected on Brownian motion. Reected Brownian motion in a domain with a...
Large deviations for stochastic Volterra equations (2000)
Nualart, David, Rovira, Carles
This paper is devoted to prove a large-deviation principle for solutions to multidimensional stochastic Volterra equations.
Evolution equation of a stochastic semigroup with white-noise drift (2000)
Nualart, David, Viens, Frederi
We study the existence and uniqueness of the solution of a function-valued stochastic evolution equation based on a stochastic semigroup whose kernel $p(s,t,y,x)$ is Brownian in $s$ and $t$.The...
On the Stochastic Burgers’ Equation in the Real Line (1999)
Gyöngy, István, Nualart, David
In this paper we establish the existence and uniqueness of an $L^2(\mathbb{R})$ -valued solution for a one-dimensional Burgers’ equation perturbed by a space–time white noise on the real line. We...
Stochastic evolution equations with random generators (1998)
Le{\'o}n, Jorge A., Nualart, David
We prove the existence of a unique mild solution for a stochastic evolution equation on a Hilbert space driven by a cylindrical Wiener process. The generator of the corresponding evolution system is...
Stochastic Differential Equations With Random Coefficients (1997)
Jorge A. Le'on, Arturo Kohatsu-higa, David Nualart
Keywords and phrases: stochastic differential equations, Stratonovich integrals 1 Supported by the DGICYT grant number PB93--0052 and UPF-Fundaci'o Universitat Nova grant P595.005 Corresponding...
Stochastic Differential Equations With Random Coefficients (1997)
Jorge A. Le'on, Arturo Kohatsu-higa, Ramon Trias Fargas, David Nualart
Keywords and phrases: stochastic differential equations, Stratonovich integrals 1 Supported by the DGICYT grant number PB93--0052 and UPF-Fundaci'o Universitat Nova grant P595.005 Corresponding...
Points of Positive Density for Smooth Functionals (1997)
Chaleyat-Maurel, Mireille; Université De Paris VI; Mcm@ccr.jussieu.fr, Nualart, David; Universitat De Barcelona; Nualart@cerber.mat.ub.es
In this paper we show that the set of points where the density of a Wiener functional is strictly positive is an open connected set, assuming some regularity conditions
Weighted Stochastic Sobolev Spaces and Bilinear SPDE's Driven by Space-time White Noise (1997)
David Nualart, Facultat De Matem`atiques, Mailing Address, Boris Rozovskii
: In this paper we develop basic elements of Malliavin calculus on a weighted L 2(OmegaGamma2 This class of generalized Wiener functionals is a Hilbert space. It turns out to be substantially smaller...
Nualart, David, Ferrante, Marco
1992/1993
Additional Utility of Insiders with Imperfect Dynamical Information
José Mª Corcuera, Peter Imkeller, Arturo Kohatsu, David Nualart
In this paper we consider an insider with privileged information that is affected by an independent noise vanishing as the revelation time approaches. At this time, information is available to every...
Completion of a Lévy market by power-jump assets
José Manuel Corcuera, David Nualart, Wim Schoutens
Except for the geometric Brownian model and the geometric Poissonian model, the general geometric Lévy market models are incomplete models and there are many equivalent martingale measures. In this...