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We observe n possibly dependent random variables, the distribution of which is presumed to be stationary even though this might not be true, and we aim at estimating the stationary distribution. We establish a non-asymptotic deviation bound…
We investigate the moment estimation for an ergodic diffusion process with unknown trend coefficient. We consider nonparametric and parametric estimation. In each case, we present a lower bound for the risk and then construct an…
One way to define the concentration of measure phenomenon is via Talagrand inequalities, also called transportation-information inequalities. That is, a comparison of the Wasserstein distance from the given measure to any other absolutely…
This paper provides a general and abstract approach to approximate ergodic regimes of Markov and Feller processes. More precisely, we show that the recursive algorithm presented in Lamberton & Pages (2002) and based on simulation algorithms…
The objective of this paper is to investigate a new numerical method for the approximation of the self-diffusion matrix of a tagged particle process defined on a grid. While standard numerical methods make use of long-time averages of…
We show the relation between processes which are modeled by a Langevin equation with multiplicative noise and infinite ergodic theory. We concentrate on a spatially dependent diffusion coefficient that behaves as ${D(x)}\sim…
In this work, we are concerned with existence and uniqueness of invariant measures for path-dependent random diffusions and their time discretizations. The random diffusion here means a diffusion process living in a random environment…
Imprecise continuous-time Markov chains are a robust type of continuous-time Markov chains that allow for partially specified time-dependent parameters. Computing inferences for them requires the solution of a non-linear differential…
We study parametric inference for ergodic diffusion processes with a degenerate diffusion matrix. Existing research focuses on a particular class of hypo-elliptic SDEs, with components split into `rough'/`smooth' and noise from rough…
We introduce a class of discrete random walk model driven by global memory effects. At any time the right-left transitions depend on the whole previous history of the walker, being defined by an urn-like memory mechanism. The characteristic…
This paper studies the theoretical underpinnings of machine learning of ergodic It\^o diffusions. The objective is to understand the convergence properties of the invariant statistics when the underlying system of stochastic differential…
Parametric estimation for diffusion processes is considered for high frequency observations over a fixed time interval. The processes solve stochastic differential equations with an unknown parameter in the diffusion coefficient. We find…
This study explores a Gaussian quasi-likelihood approach for estimating parameters of diffusion processes with Markovian regime switching. Assuming the ergodicity under high-frequency sampling, we will show the asymptotic normality of the…
Canonical characterization techniques that rely upon mean squared displacement ($\mathrm{MSD}$) break down for non-ergodic processes, making it challenging to characterize anomalous diffusion from an individual time-series measurement.…
We prove concentration inequalities and associated PAC bounds for continuous- and discrete-time additive functionals for possibly unbounded functions of multivariate, nonreversible diffusion processes. Our analysis relies on an approach via…
This study examines the statistical nature of instantaneous scalar concentration in an elevated point-source plume (neutral or buoyant) dispersing within a turbulent boundary layer. Using high-frequency long-duration experimental…
Motivated by the task of computing normalizing constants and importance sampling in high dimensions, we study the dimension dependence of fluctuations for additive functionals of time-inhomogeneous Langevin-type diffusions on…
Score-based diffusion models have emerged as powerful techniques for generating samples from high-dimensional data distributions. These models involve a two-phase process: first, injecting noise to transform the data distribution into a…
A general theory of efficient estimation for ergodic diffusion processes sampled at high frequency with an infinite time horizon is presented. High frequency sampling is common in many applications, with finance as a prominent example. The…
We consider statistical inference in factor analysis for ergodic and non-ergodic diffusion processes from discrete observations. Factor model based on high frequency time series data has been mainly discussed in the field of high…