203 citations · 730 across the 42 of their papers we have counts for
28 papers · 1 filter
Asymptotics of Yule's nonsense correlation for Ornstein-Uhlenbeck paths: The correlated case
Soukaina Douissi, Philip Ernst, Frederi Viens
We study the continuous-time version of the empirical correlation coefficient between the paths of two possibly correlated Ornstein-Uhlenbeck processes, known as Yule's nonsense co…
The isometry of symmetric-Stratonovich integrals w.r.t. Fractional Brownian motion
Alberto Ohashi, Francesco Russo, Frederi Viens
In this work, we present a detailed analysis on the exact expression of the -norm of the symmetric-Stratonovich stochastic integral driven by a multi-dimensional fractional Br…
Irregularity scales for Gaussian processes: Hausdorff dimensions and hitting probabilities
Youssef Hakiki, Frederi Viens
Let be a -dimensional Gaussian process in , where the component are independent copies of a scalar Gaussian process on with a given general variance fun…
Hausdorff dimensions and Hitting probabilities for some general Gaussian processes
Frederi Viens, Mohamed Erraoui, Youssef Hakiki
Let be a -dimensional Gaussian process on , where the component are independents copies of a scalar Gaussian process on with a given general…
Asymptotics of Yule's nonsense correlation for Ornstein-Uhlenbeck paths: a Wiener chaos approach
Soukaina Douissi, Frederi G. Viens, Khalifa Es-Sebaiy
In this paper, we study the distribution of the so-called "Yule's nonsense correlation statistic" on a time interval for a time horizon , when is large, for a pai…
Yule's "nonsense correlation" for Gaussian random walks
Philip A. Ernst, Dongzhou Huang, Frederi G. Viens
The purpose of this paper is to provide an exact formula for the second moment of the empirical correlation of two independent Gaussian random walks as well as implicit formulas fo…
Poisson Approximation to the Convolution of Power Series Distributions
A. N. Kumar, P. Vellaisamy, F. Viens
In this article, we obtain, for the total variance distance, the error bounds between Poisson and convolution of power series distributions via Stein's method. This provides a unif…
AR(1) processes driven by second-chaos white noise: Berry-Esséen bounds for quadratic variation and parameter estimation
Soukaina Douissi, Khalifa Es-Sebaiy, Fatimah Alshahrani +1
In this paper, we study the asymptotic behavior of the quadratic variation for the class of AR(1) processes driven by white noise in the second Wiener chaos. Using tools from the a…
A Martingale Approach for Fractional Brownian Motions and Related Path Dependent PDEs
Frederi Viens, Jianfeng Zhang
In this paper we study dynamic backward problems, with the computation of conditional expectations as a main objective, in a framework where the (forward) state process satisfies a…
Berry-Esséen bounds for parameter estimation of general Gaussian processes
Soukaina Douissi, Khalifa Es-Sebaiy, Frederi G. Viens
We study rates of convergence in central limit theorems for the partial sum of squares of general Gaussian sequences, using tools from analysis on Wiener space. No assumption of st…
A third-moment theorem and precise asymptotics for variations of stationary Gaussian sequences
Leo Neufcourt, Frederi Viens
In two new papers (Bierme et al., 2013) and (Nourdin and Peccati, 2015), sharp general quantitative bounds \ are given to complement the well-known fourth moment theorem of Nualart…
Anderson polymer in a fractional Brownian environment: asymptotic behavior of the partition function
Kamran Kalbasi, Thomas S. Mountford, Frederi G. Viens
We consider the Anderson polymer partition function where is a…
Parameter estimation for SDEs related to stationary Gaussian processes
Khalifa Es-Sebaiy, Frederi G. Viens
In this paper, we study central and non-central limit theorems for partial sum of functionals of general stationary Gaussian fields. We apply our result to study drift parameter es…
Parameter Estimation for a partially observed Ornstein-Uhlenbeck process with long-memory noise
Brahim El Onsy, Khalifa Es-Sebaiy, Frederi G. Viens
\noindent \textbf{Abstract}: We consider the parameter estimation problem for the Ornstein-Uhlenbeck process driven by a fractional Ornstein-Uhlenbeck process , i.e. the pai…
Gaussian and non-Gaussian processes of zero power variation, and related stochastic calculus
Francesco Russo, Frederi Viens
We consider a class of stochastic processes defined by for , where is a square-integr…
Comparison inequalities on Wiener space
Ivan Nourdin, Giovanni Peccati, Frederi Viens
We define a covariance-type operator on Wiener space: for F and G two random variables in the Gross-Sobolev space of random variables with a square-integrable Malliavin d…
Hitting probabilities for general Gaussian processes
E. Nualart, F. Viens
For a scalar Gaussian process on with a prescribed general variance function and a canonical…
General upper and lower tail estimates using Malliavin calculus and Stein's equations
Richard Eden, Frederi Viens
Following a strategy recently developed by Ivan Nourdin and Giovanni Peccati, we provide a general technique to compare the tail of a given random variable to that of a reference d…
Variations and Hurst index estimation for a Rosenblatt process using longer filters
Alexandra Chronopoulou, Ciprian Tudor, Frederi Viens
The Rosenblatt process is a self-similar non-Gaussian process which lives in second Wiener chaos, and occurs as the limit of correlated random sequences in so-called \textquotedbll…
Gaussian and non-Gaussian processes of zero power variation
Francesco Russo, Frederi Viens
This paper considers the class of stochastic processes which are Volterra convolutions of a martingale . When is Brownian motion, is Gaussian, and the class includes…
Stein's lemma, Malliavin calculus, and tail bounds, with application to polymer fluctuation exponent
Frederi G. Viens
We consider a random variable X satisfying almost-sure conditions involving G:=<DX,-DL^{-1}X> where DX is X's Malliavin derivative and L^{-1} is the inverse Ornstein-Uhlenbeck oper…
Superdiffusivity for a Brownian polymer in a continuous Gaussian environment
Sérgio Bezerra, Samy Tindel, Frederi Viens
This paper provides information about the asymptotic behavior of a one-dimensional Brownian polymer in random medium represented by a Gaussian field on ${\mathbb{R}}_+\times{\m…
Density estimates and concentration inequalities with Malliavin calculus
Ivan Nourdin, Frederi G. Viens
We show how to use the Malliavin calculus to obtain density estimates of the law of general centered random variables. In particular, under a non-degeneracy condition, we prove and…
Self-similarity parameter estimation and reproduction property for non-Gaussian Hermite processes
Alexandra Chronopoulou, Frederi Viens, Ciprian Tudor
We consider the class of all the Hermite processes of order and with Hurst parameter . The pr…