The properties of fractional Gaussian Process and their Applications
Y Chen, Y Li - arXiv preprint arXiv:2309.10415, 2023 - arxiv.org
The process $(G_t) _ {t\in [0, T]} $ is referred to as a fractional Gaussian process if the first-
order partial derivative of the difference between its covariance function and that of the …
order partial derivative of the difference between its covariance function and that of the …
Kolmogorov bounds in the CLT of the LSE for Gaussian Ornstein Uhlenbeck processes
MF Balde, R Belfadli, K Es-Sebaiy - Stochastics and Dynamics, 2023 - World Scientific
In this paper, we consider the Ornstein–Uhlenbeck (OU) process defined as solution to the
equation d X t=− 𝜃 X tdt+ d G t, X 0= 0, where {G t, t≥ 0} is a Gaussian process with …
equation d X t=− 𝜃 X tdt+ d G t, X 0= 0, where {G t, t≥ 0} is a Gaussian process with …
Statistical inference for the first-order autoregressive process with the fractional Gaussian noise
Y Huang, W Xiao, X Yu - Quantitative Finance, 2024 - Taylor & Francis
While the statistical inference of first-order autoregressive processes driven by independent
and identically distributed noises has a long history, the statistical analysis for first-order …
and identically distributed noises has a long history, the statistical analysis for first-order …
An Improved Berry-Esseen Bound of Least Squares Estimation for Fractional Ornstein-Uhlenbeck Processes
Y Chen, X Gu - arXiv preprint arXiv:2210.00420, 2022 - arxiv.org
The aim of this paper is twofold. First, it offers a novel formula to calculate the inner product
of the bounded variation function in the Hilbert space $\mathcal {H} $ associated with the …
of the bounded variation function in the Hilbert space $\mathcal {H} $ associated with the …
Chebyshev--Hermite Polynomials and Distributions of Polynomials in Gaussian Random Variables
VI Bogachev - Theory of Probability & Its Applications, 2022 - SIAM
\bad This paper gives a survey of several directions of research connected with Chebyshev--
Hermite polynomials on finite-dimensional and infinite-dimensional spaces, in particular, of …
Hermite polynomials on finite-dimensional and infinite-dimensional spaces, in particular, of …
Wasserstein bounds in CLT of approximative MCE and MLE of the drift parameter for Ornstein-Uhlenbeck processes observed at high frequency
This paper deals with the rate of convergence for the central limit theorem of estimators of
the drift coefficient, denoted θ, for the Ornstein-Uhlenbeck process X:={X t, t≥ 0} observed at …
the drift coefficient, denoted θ, for the Ornstein-Uhlenbeck process X:={X t, t≥ 0} observed at …
Distributions of second order polynomials in Gaussian random variables
ED Kosov - Mathematical Notes, 2022 - Springer
In this paper, we study bounds for the total variation distance between distributions of
second order polynomials in normal random variables provided that they essentially depend …
second order polynomials in normal random variables provided that they essentially depend …
Wasserstein Bounds in the CLT of the MLE for the Drift Coefficient of a Stochastic Partial Differential Equation
In this paper, we are interested in the rate of convergence for the central limit theorem of the
maximum likelihood estimator of the drift coefficient for a stochastic partial differential …
maximum likelihood estimator of the drift coefficient for a stochastic partial differential …
Parameter estimation for fractional stochastic heat equations: Berry-Ess\'een bounds in CLTs
S Douissi, F Alshahrani - arXiv preprint arXiv:2409.05416, 2024 - arxiv.org
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 first part …
an additive space-time noise using the Maximum likelihood estimator (MLE). In the first part …
Gaussian and hermite Ornstein–Uhlenbeck processes
K Es-Sebaiy - Stochastic Analysis and Applications, 2023 - Taylor & Francis
In the present paper we study the asymptotic behavior of the auto-covariance function for
Ornstein–Uhlenbeck (OU) processes driven by Gaussian noises with stationary and non …
Ornstein–Uhlenbeck (OU) processes driven by Gaussian noises with stationary and non …