Related papers: Adaptive test for ergodic diffusions plus noise
Existing tests for factorial designs in the nonparametric case are based on hypotheses formulated in terms of distribution functions. Typical null hypotheses, however, are formulated in terms of some parameters or effect measures,…
This letter reports on a new method of analysing experimentally gained time series with respect to different types of noise involved, namely, we show that it is possible to differentiate between dynamical and measurement noise. This method…
In this work we perform rigorous small noise expansions to study the impact of stochastic forcing on the behaviour of planar travelling wave solutions to reaction-diffusion equations on cylindrical domains. In particular, we use a…
As machine learning models are deployed ever more broadly, it becomes increasingly important that they are not only able to perform well on their training distribution, but also yield accurate predictions when confronted with distribution…
For the sparse vector model, we consider estimation of the target vector, of its L2-norm and of the noise variance. We construct adaptive estimators and establish the optimal rates of adaptive estimation when adaptation is considered with…
In this note, we consider a Stochastic Differential Equation under a strong confluence and Lipschitz continuity assumption of the coefficients. For the unique stationary solution, we study the rate of convergence of its empirical measure…
We introduce a new class of generative diffusion models that, unlike conventional denoising diffusion models, achieve a time-homogeneous structure for both the noising and denoising processes, allowing the number of steps to adaptively…
We study the properties of several likelihood-based statistics commonly used in testing for the presence of a known signal under a mixture model with known background, but unknown signal fraction. Under the null hypothesis of no signal, all…
Statistical inference for stochastic processes has advanced significantly due to applications in diverse fields, but challenges remain in high-dimensional settings where parameters are allowed to grow with the sample size. This paper…
A longstanding problem of existing empirical process-based tests for regressions is that when the number of covariates is greater than one, they either have no tractable limiting null distributions or are not omnibus. To attack this…
The main purpose of this paper is to propose an ergodic theoretic approach to the study of entire holomorphic curves. Brody curves are one-Lipschitz holomorphic maps from the complex plane to the complex projective space. They naturally…
We study here the random diffusion model. This is a continuum model for a conserved scalar density field $\phi$ driven by diffusive dynamics. The interesting feature of the dynamics is that the {\it bare} diffusion coefficient $D$ is…
We study small perturbations of diffusion processes in $\mathbb{R}^d$ that leave invariant a finite collection of hypersurfaces. Each surface is assumed to be repelling for the unperturbed process, and the unperturbed motion on each of the…
We develop joint confidence regions for linear regression coefficients when the regressors and errors are jointly stationary and ergodic with unspecified serial dependence. The method applies random smoothing, using an independent auxiliary…
Electrocardiography (ECG) signals are frequently degraded by noise, limiting their clinical reliability in both conventional and wearable settings. Existing methods for addressing ECG noise, relying on artifact classification or denoising,…
Temporal data such as time series can be viewed as discretized measurements of the underlying function. To build a generative model for such data we have to model the stochastic process that governs it. We propose a solution by defining the…
In this article, we discuss ergodicity properties of a diffusion process given through an It\^{o} stochastic differential equation. We identify conditions on the drift and diffusion coefficients which result in sub-geometric ergodicity of…
In this thesis we study adaptive nonparametric regression with noise misspecification and the complexity of approximation of random fields in dependence of the dimension. First, we consider the problem of pointwise estimation in…
Time series often exhibit non-ergodic behaviour that complicates forecasting and inference. This article proposes a likelihood-based approach for estimating ergodicity transformations that addresses such challenges. The method is broadly…
We study a simple stochastic differential equation that models the dispersion of close heavy particles moving in a turbulent flow. In one and two dimensions, the model is closely related to the one-dimensional stationary Schroedinger…