Related papers: Asymptotic for the quantization error for a Wiener…
For a theoretical understanding of the reactivity of complex chemical systems, relative energies of stationary points on potential energy hypersurfaces need to be calculated to high accuracy. Due to the large number of intermediates present…
A reliable method for characterizing quantum operations that is suitable for improving and validating their accuracies is indispensable for realizing a practical quantum computer. Known methods are still not sufficient because they lack…
The theory of Gaussian quantum fluctuations around classical steady states in nonlinear quantum-optical systems (also known as standard linearization) is a cornerstone for the analysis of such systems. Its simplicity, together with its…
Missing values with mixed data types is a common problem in a large number of machine learning applications such as processing of surveys and in different medical applications. Recently, Gaussian copula models have been suggested as a means…
Gaussian process regression is used throughout statistics and machine learning for prediction and uncertainty quantification. A Gaussian process is specified by its mean and covariance functions. Many covariance functions, including…
Gaussian processes (GPs) are widely used in non-parametric Bayesian modeling, and play an important role in various statistical and machine learning applications. In a variety tasks of uncertainty quantification, generating random sample…
Asymptotic expansion is presented for an estimator of the Hurst coefficient of a fractional Brownian motion. For this, a recently developed theory of asymptotic expansion of the distribution of Wiener functionals is applied. The effects of…
This paper deals with the local semiclassical asymptotics of a quantum evolution operator in the Berezin-Toeplitz scheme, when both time and phase space variables are subject to appropriate scalings in the neighborhood of the graph of the…
We consider functions of Wiener--Hopf type operators on the Hilbert space $L^2(\mathbb R^d)$. It has been known for a long time that the quasi-classical asymptotics for traces of resulting operators strongly depend on the smoothness of the…
The Gaussian integral operator arises naturally as a local Euclidean approximation of the heat semigroup on a Riemannian manifold and plays a pivotal role in the analysis of graph Laplacians, particularly within the frameworks of manifold…
Measurements are central in all quantitative sciences, and a fundamental challenge is to make observations without systematic measurement errors. This holds in particular for quantum information processing, where other error sources, such…
Bayesian learning using Gaussian processes provides a foundational framework for making decisions in a manner that balances what is known with what could be learned by gathering data. In this dissertation, we develop techniques for…
This article shortly introduces Gaussian processes (GP) as a new approach for modelling time series in the field of blazar physics. In the second part of the paper, recent results from an application of GP modelling to the multi-wavelength…
This paper establishes expectation and variance asymptotics for statistics of the Poisson--Voronoi approximation of general sets, as the underlying intensity of the Poisson point process tends to infinity. Statistics of interest include…
We consider statistical models where functional data are artificially contaminated by independent Wiener processes in order to satisfy privacy constraints. We show that the corrupted observations have a Wiener density which determines the…
Gaussian processes (GPs) are a class of Kernel methods that have shown to be very useful in geoscience and remote sensing applications for parameter retrieval, model inversion, and emulation. They are widely used because they are simple,…
Gaussian processes are probabilistic models that are commonly used as functional priors in machine learning. Due to their probabilistic nature, they can be used to capture the prior information on the statistics of noise, smoothness of the…
We compute the Wiener chaos decomposition of the signature for a class of Gaussian processes, which contains fractional Brownian motion (fBm) with Hurst parameter H in (1/4, 1). At level 0, our result yields an expression for the expected…
Starting from the resurgence equation discovered by Berry and Howls [M. V. Berry and C. Howls "Hyperasymptotics for integrals with saddles," Proc. R. Soc. Lond. A 434, 657-675 (1991)], the Weniger transformation is here proposed as a…
The impact of measurement imperfections on quantum metrology protocols has not been approached in a systematic manner so far. In this work, we tackle this issue by generalising firstly the notion of quantum Fisher information to account for…