8 papers
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…
Parameter estimation for fractional stochastic heat equations : Berry-Esséen bounds in CLTs
Soukaina Douissi, Fatimah Alshahrani
The aim of this work is to estimate the drift coefficient of a fractional heat equation driven by an additive space-time noise using the Maximum likelihood estimator (MLE). In the…
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…
Berry-Esseen bounds of second moment estimators for Gaussian processes observed at high frequency
Soukaina Douissi, Khalifa Es-Sebaiy, George Kerchev +1
Let be a stationary Gaussian process. We study two estimators of , namely , and $\wi…
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…
Mean-field anticipated BSDEs driven by fractional Brownian motion and related stochastic control problem
Soukaina Douissi, Jiaqiang Wen, Yufeng Shi
In this paper, we focus on mean-field anticipated backward stochastic differential equations (MF-BSDEs, for short) driven by fractional Brownian motion with Hurst parameter H>1/2.…
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…
Mean-field optimal control problem of SDDEs driven by fractional Brownian motion
Nacira Agram, Soukaina Douissi, Astrid Hilbert
We consider a mean-field optimal control problem for stochastic differential equations with delay driven by fractional Brownian motion with Hurst parameter greater than one half. S…