Ciprian Tudor

Limits of bifractional Brownian noises (2008)

Let $B^{H,K}=\left (B^{H,K}_{t}, t\geq 0\right )$ be a bifractional Brownian motion with two parameters $H\in (0,1)$ and $K\in(0,1]$. The main result of this paper is that the increment process...

Limits of bifractional Brownian noises (2008)

Let $B^{H,K}=\left (B^{H,K}_{t}, t\geq 0\right )$ be a bifractional Brownian motion with two parameters $H\in (0,1)$ and $K\in(0,1]$. The main result of this paper is that the increment process...

Lévy processes and Itô-Skorohod integrals (2008)

Let $B^{H,K}=(B^{H,K}_{t}, t\geq 0)$ be a bifractional Brownian motion with two parameters $H\in (0,1)$ and $K\in(0,1]$. The main result of this paper is that the increment process generated by the...

Lévy processes and Itô-Skorohod integrals (2008)

We study Skorohod integral processes on Lévy spaces and we prove an equivalence between this class of processes and the class of Itô-Skorohod processes. Using this equivalence we introduce a...

Analysis of the Rosenblatt process (2008)

We study Skorohod integral processes on Lévy spaces and we prove an equivalence between this class of processes and the class of Itô-Skorohod processes. Using this equivalence we introduce a...

The Stochastic Heat Equation with a Fractional-Colored Noise: Existence of the Solution (2008)

We analyze {\em the Rosenblatt process } which is a selfsimilar process with stationary increments and which appears as limit in the so-called {\em Non Central Limit Theorem } (Dobrushin and Major...

Balan, Raluca, Tudor, Ciprian

In this article we consider the stochastic heat equation $u_{t}-\Delta u=\dot B$ in $(0,T) \times \bR^d$, with vanishing initial conditions, driven by a Gaussian noise $\dot B$ which is fractional in...

On the convergence to the multiple Wiener-Ito integral (2008)

Bardina, Xavier, Jolis, Maria, Tudor, Ciprian

We study the convergence to the multiple Wiener-It\^{o} integral from processes with absolutely continuous paths. More precisely, consider a family of processes, with paths in the Cameron-Martin...

On the convergence to the multiple Wiener-Ito integral (2008)

Bardina, Xavier, Jolis, Maria, Tudor, Ciprian

We study the convergence to the multiple Wiener-It\^{o} integral from processes with absolutely continuous paths. More precisely, consider a family of processes, with paths in the Cameron-Martin...

The Stochastic Heat Equation with a Fractional-Colored Noise: Existence of the Solution (2008)

Balan, Raluca, Tudor, Ciprian

In this article we consider the stochastic heat equation $u_{t}-\Delta u=\dot B$ in $(0,T) \times \bR^d$, with vanishing initial conditions, driven by a Gaussian noise $\dot B$ which is fractional in...

Analysis of the Rosenblatt process (2008)

Chronopoulou, Alexandra, Tudor, Ciprian, Viens, Frederi

We analyze {\em the Rosenblatt process } which is a selfsimilar process with stationary increments and which appears as limit in the so-called {\em Non Central Limit Theorem } (Dobrushin and Major...

We consider the class of all the Hermite processes $(Z_{t}^{(q,H)})_{t\in \lbrack 0,1]}$ of order $q\in \mathbf{N}^{\ast }$ and with Hurst parameter $% H\in (\frac{1}{2},1)$. The process $Z^{(q,H)}$...

Chronopoulou, Alexandra, Tudor, Ciprian, Viens, Frederi

We consider the class of all the Hermite processes $(Z_{t}^{(q,H)})_{t\in \lbrack 0,1]}$ of order $q\in \mathbf{N}^{\ast }$ and with Hurst parameter $% H\in (\frac{1}{2},1)$. The process $Z^{(q,H)}$...

Chronopoulou, Alexandra, Tudor, Ciprian, Viens, Frederi

We consider the class of all the Hermite processes $(Z_{t}^{(q,H)})_{t\in \lbrack 0,1]}$ of order $q\in \mathbf{N}^{\ast}$ and with Hurst parameter $% H\in ({1/2},1)$. The process $Z^{(q,H)}$ is...

Ito formula for the infinite dimensional fractional Brownian motion (2008)

Ito formula for the infinite dimensional fractional Brownian motion (2008)

We introduce the stochastic integration with respect to the infinite-dimensional fractional Brownian motion. Using the techniques of the anticipating stochastic calculus, we derive an It\^o formula...

Anticipating integrals and martingales on the Poisson space (2008)

We introduce the stochastic integration with respect to the infinite-dimensional fractional Brownian motion. Using the techniques of the anticipating stochastic calculus, we derive an It\^o formula...

Anticipating integrals and martingales on the Poisson space (2008)

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)

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...

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...

The law of a stochastic integral with two independent fractional Brownian motions (2008)

Bardina, Xavier, Tudor, Ciprian

Using the tools of the stochastic integration with respect to the fractional Brownian motion, we obtain the expression of the characteristic function of the random variable $\int_{0}^{1}B^{\alpha...

Parameter estimation for stochastic equations with additive fractional Brownian sheet (2008)

Sample Path Properties of Bifractional Brownian Motion (2008)

We study the maximum likelihood estimator for stochastic equations with additive fractional Brownian sheet. We use the Girsanov transform for the the two-parameter fractional Brownian motion, as well...

Sample Path Properties of Bifractional Brownian Motion (2008)

Let BH, K={BH, K(t), t \in R +} be a bifractional Brownian motion in R d. We prove that BH, K is strongly locally non-deterministic. Applying this property and a stochastic...

Parameter estimation for stochastic equations with additive fractional Brownian sheet (2008)

Let BH, K={BH, K(t), t \in R +} be a bifractional Brownian motion in R d. We prove that BH, K is strongly locally non-deterministic. Applying this property and a stochastic...

The law of a stochastic integral with two independent fractional Brownian motions (2008)

We study the maximum likelihood estimator for stochastic equations with additive fractional Brownian sheet. We use the Girsanov transform for the the two-parameter fractional Brownian motion, as well...

Bardina, Xavier, Tudor, Ciprian

Using the tools of the stochastic integration with respect to the fractional Brownian motion, we obtain the expression of the characteristic function of the random variable $\int_{0}^{1}B^{\alpha...

Multidimensional bifractional Brownian motion: Ito and Tanaka formulas (2008)

Wiener integrals with respect to the Hermite process and a Non-Central Limit Theorem (2008)

Using the Malliavin calculus with respect to Gaussian processes and the multiple stochastic integrals we derive Itô's and Tanaka's formulas for the $d$-dimensional bifractional Brownian motion.

Wiener integrals with respect to the Hermite process and a Non-Central Limit Theorem (2008)

We introduce Wiener integrals with respect to the Hermite process and we prove a Non-Central Limit Theorem in which this integral appears as limit. As an example, we study a generalization of the...

Multidimensional bifractional Brownian motion: Ito and Tanaka formulas (2008)

We introduce Wiener integrals with respect to the Hermite process and we prove a Non-Central Limit Theorem in which this integral appears as limit. As an example, we study a generalization of the...

Occupation densities for certain processes related to fractional Brownian motion (2008)

Using the Malliavin calculus with respect to Gaussian processes and the multiple stochastic integrals we derive Itô's and Tanaka's formulas for the $d$-dimensional bifractional Brownian motion.

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...

On the convergence to the multiple Wiener-Ito integral (2007)

Bardina, Xavier, Jolis, Maria, Tudor, Ciprian

We study the convergence to the multiple Wiener-It\^{o} integral from processes with absolutely continuous paths. More precisely, consider a family of processes, with paths in the Cameron-Martin...

Maximum likelihood estimators and random walks in long memory models (2007)

Bertin, Karine, Torres, Soledad, Tudor, Ciprian

We consider statistical models driven by Gaussian and non-Gaussian self-similar processes with long memory and we construct maximum likelihood estimators (MLE) for the drift parameter. Our approach...

Maximum likelihood estimators and random walks in long memory models (2007)

Bertin, Karine, Torres, Soledad, Tudor, Ciprian

We consider statistical models driven by Gaussian and non-Gaussian self-similar processes with long memory and we construct maximum likelihood estimators (MLE) for the drift parameter. Our approach...

Maximum likelihood estimators and random walks in long memory models (2007)

Bertin, Karine, Torres, Soledad, Tudor, Ciprian

We consider statistical models driven by Gaussian and non-Gaussian self-similar processes with long memory and we construct maximum likelihood estimators (MLE) for the drift parameter. Our approach...

Central and non-central limit theorems for weighted power variations of fractional Brownian motion (2007)

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...

Central and non-central limit theorems for weighted power variations of fractional Brownian motion (2007)

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...

Ito formula for the two parameter fractional Brownian motion using the extended divergence integral (2007)

Ito formula for the two parameter fractional Brownian motion using the extended divergence integral (2007)

We develop a stochastic calculus of divergence type with respect to the fractional Brownian sheet (fBs) with any Hurst parameters in (0; 1) and beyond the fractional scale. We define stochastic...

Some linear fractional stochastic equations (2007)

We develop a stochastic calculus of divergence type with respect to the fractional Brownian sheet (fBs) with any Hurst parameters in (0; 1) and beyond the fractional scale. We define stochastic...

Nourdin, Ivan, Tudor, Ciprian

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...

On the bifractional Brownian motion (2007)

Russo, Francesco, Tudor, Ciprian

This paper is devoted to analyze several properties of the bifractional Brownian motion introduced by Houdr\'e and Villa. This process is a self-similar Gaussian process depending on two parameters...

On the equivalence of multiparameter Gaussian processes (2007)

On the equivalence of multiparameter Gaussian processes (2007)

Our purpose is to characterize the multiparameter Gaussian processes, that is Gaussian sheets, that are equivalent in law to the Brownian sheet and to the fractional Brownian sheet. We survey...

On the bifractional Brownian motion (2007)

Our purpose is to characterize the multiparameter Gaussian processes, that is Gaussian sheets, that are equivalent in law to the Brownian sheet and to the fractional Brownian sheet. We survey...

Russo, Francesco, Tudor, Ciprian

This paper is devoted to analyze several properties of the bifractional Brownian motion introduced by Houdr\'e and Villa. This process is a self-similar Gaussian process depending on two parameters...

Some linear fractional stochastic equations (2007)

Nourdin, Ivan, Tudor, Ciprian

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...

Variations and estimators for the selfsimilarity order through Malliavin calculus (2007)

Variations and estimators for the selfsimilarity order through Malliavin calculus (2007)

Using multiple stochastic integrals, we analyze the asymptotic behavior of quadratic variations for Gaussian and non-Gaussian selfsimilar processes. We apply our results to the study of statistical...

Sample Path Properties of Bifractional Brownian Motion (2007)

Using multiple stochastic integrals, we analyze the asymptotic behavior of quadratic variations for Gaussian and non-Gaussian selfsimilar processes. We apply our results to the study of statistical...

Statistical aspects of the fractional stochastic calculus (2007)

Let $B^{H, K}= \big\{B^{H, K}(t),\, t \in \R_+ \big\}$ be a bifractional Brownian motion in $\R^d$. We prove that $B^{H, K}$ is strongly locally nondeterministic. Applying this property and a...

Statistical aspects of the fractional stochastic calculus (2007)

We apply the techniques of stochastic integration with respect to the fractional Brownian motion and the Gaussian theory of regularity and supremum estimation to study the maximum likelihood...

Variations and estimators for the selfsimilarity order through Malliavin calculus (2007)

We apply the techniques of stochastic integration with respect to the fractional Brownian motion and the Gaussian theory of regularity and supremum estimation to study the maximum likelihood...

Wiener integrals, Malliavin calculus and covariance measure structure (2007)

Using multiple stochastic integrals, we analyze the asymptotic behavior of quadratic variations for Gaussian and non-Gaussian selfsimilar processes. We apply our results to the study of statistical...

Wiener integrals, Malliavin calculus and covariance measure structure (2007)

We introduce the notion of {\em covariance measure structure} for square integrable stochastic processes. We define Wiener integral, we develop a suitable formalism for stochastic calculus of...

Donsker theorem for the Rosenblatt process and a binary market model (2007)

We introduce the notion of {\em covariance measure structure} for square integrable stochastic processes. We define Wiener integral, we develop a suitable formalism for stochastic calculus of...

Torres, Soledad, Tudor, Ciprian

In this paper, we prove a Donsker type approximation theorem for the Rosenblatt process, which is a selfsimilar stochastic process exhibiting long range dependence. By using numerical results and...

Donsker theorem for the Rosenblatt process and a binary market model (2007)

Tudor, Ciprian, Torres, Soledad

In this paper, we prove a Donsker type approximation theorem for the Rosenblatt process, which is a selfsimilar stochastic process exhibiting long range dependence. By using numerical results and...

Multidimensional bifractional Brownian motion: Ito and Tanaka formulas (2007)

Tudor, Ciprian, Es-Sebaiy, Khalifa

Using the Malliavin calculus with respect to Gaussian processes and the multiple stochastic integrals we derive It\^{o}'s and Tanaka's formulas for the $d$-dimensional bifractional Brownian motion.

The Stochastic Heat Equation with a Fractional-Colored Noise: Existence of the Solution (2007)

Balan, Raluca, Tudor, Ciprian

In this article we consider the stochastic heat equation $u_{t}-\Delta u=\dot B$ in $(0,T) \times \bR^d$, with vanishing initial conditions, driven by a Gaussian noise $\dot B$ which is fractional in...

Donsker theorem for the Rosenblatt process and a binary market model (2007)

Torres, Soledad, Tudor, Ciprian

In this paper, we prove a Donsker type approximation theorem for the Rosenblatt process, which is a selfsimilar stochastic process exhibiting long range dependence. By using numerical results and...

Wiener integrals, Malliavin calculus and covariance measure structure (2007)

Sample Path Properties of Bifractional Brownian Motion (2006)

We introduce the notion of {\em covariance measure structure} for square integrable stochastic processes. We define Wiener integral, we develop a suitable formalism for stochastic calculus of...

Sample Path Properties of Bifractional Brownian Motion (2006)

Let $B^{H, K}= \big\{B^{H, K}(t),\, t \in \R_+ \big\}$ be a bifractional Brownian motion in $\R^d$. We prove that $B^{H, K}$ is strongly locally nondeterministic. Applying this property and a...

Sample Path Properties of Bifractional Brownian Motion (2006)

Let $B^{H, K}= \big\{B^{H, K}(t),\, t \in \R_+ \big\}$ be a bifractional Brownian motion in $\R^d$. We prove that $B^{H, K}$ is strongly locally nondeterministic. Applying this property and a...

Wiener integrals, Malliavin calculus and covariance measure structure (2006)

Let $B^{H, K}= \big\{B^{H, K}(t), t \in \R_+ \big\}$ be a bifractional Brownian motion in $\R^d$. We prove that $B^{H, K}$ is strongly locally nondeterministic. Applying this property and a...

Wiener integrals, Malliavin calculus and covariance measure structure (2006)

We introduce the notion of {\em covariance measure structure} for square integrable stochastic processes. We define Wiener integral, we develop a suitable formalism for stochastic calculus of...

Wiener integrals, Malliavin calculus and covariance measure structure (2006)

We introduce the notion of {\em covariance measure structure} for square integrable stochastic processes. We define Wiener integral, we develop a suitable formalism for stochastic calculus of...

Anticipating integrals and martingales on the Poisson space (2005)

We introduce the notion of {\em covariance measure structure} for square integrable stochastic processes. We define Wiener integral, we develop a suitable formalism for stochastic calculus of...

Anticipating integrals and martingales on the Poisson space (2005)

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...