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Related papers: Total variation estimates for the TCP process

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This paper provides estimates for the convergence rate of the total variation distance in the framework of the Breuer-Major theorem, assuming some smoothness properties of the underlying function. The results are proved by applying new…

Probability · Mathematics 2018-07-26 David Nualart , Hongjuan Zhou

Assuming that a threshold Ornstein-Uhlenbeck process is observed at discrete time instants, we propose generalized moment estimators to estimate the parameters. Our theoretical basis is the celebrated ergodic theorem. To use this theorem we…

Statistics Theory · Mathematics 2020-11-24 Yaozhong Hu , Yuejuan Xi

This paper presents different approaches, based on functional inequalities, to study the speed of convergence in total variation distance of ergodic diffusion processes with initial law satisfying a given integrability condition. To this…

Probability · Mathematics 2007-05-23 Patrick Cattiaux , Arnaud Guillin

Markov chains and diffusion processes are indispensable tools in machine learning and statistics that are used for inference, sampling, and modeling. With the growth of large-scale datasets, the computational cost associated with simulating…

Statistics Theory · Mathematics 2017-08-31 Jonathan H. Huggins , James Zou

We prove the convergence of the law of grid-valued random walks, which can be seen as time-space Markov chains, to the law of a general diffusion process. This includes processes with sticky features, reflecting or absorbing boundaries and…

Probability · Mathematics 2024-11-15 Alexis Anagnostakis , Antoine Lejay , Denis Villemonais

We provide non-asymptotic error bounds in the path Wasserstein distance with quadratic integral cost between suitable functionals of the telegraph process and the corresponding functional of Brownian motion with explicit diffusivity…

Probability · Mathematics 2025-09-16 Gerardo Barrera , Jani Lukkarinen , Mikko S. Pakkanen

We study the average $p-$Wasserstein distance between a finite sample of an infinite hyperuniform point process on $\mathbb{R}^2$ and its mean for any $p\geq 1$. The average Wasserstein transport cost is shown to be bounded from above and…

Probability · Mathematics 2024-07-23 Raphael Butez , Sandrine Dallaporta , David García-Zelada

We show the variational convergence of an irreversible Markov jump process describing a finite stochastic particle system to the solution of a countable infinite system of deterministic time-inhomogeneous quadratic differential equations…

Analysis of PDEs · Mathematics 2025-07-08 Jasper Hoeksema , Chun Yin Lam , André Schlichting

The cutoff phenomenon describes the case when an abrupt transition occurs in the convergence of a Markov chain to its equilibrium measure. There are various metrics which can be used to measure the distance to equilibrium, each of which…

Probability · Mathematics 2018-01-29 Jonathan Hermon , Hubert Lacoin , Yuval Peres

We study fluctuations of mean-field interacting particle systems around their McKean--Vlasov limit. Our main result provides a uniform-in-time quantitative central limit theorem for the fluctuation process, with convergence rate of order…

Probability · Mathematics 2026-05-06 Solesne Bourguin , Konstantinos Spiliopoulos

We consider the extreme value statistics of correlated random variables that arise from a Langevin equation. Recently, it was shown that the extreme values of the Ornstein-Uhlenbeck process follow a different distribution than those…

Statistical Mechanics · Physics 2021-08-17 Lior Zarfaty , Eli Barkai , David A. Kessler

The purpose of this paper is to analyze the distribution distance between random vectors derived from the magnitude of the analytic wavelet transform of the squared envelopes of Gaussian processes and their large-scale limits. When the…

Probability · Mathematics 2024-09-05 Gi-Ren Liu

We present upper bounds for the Wasserstein distance of order $p$ between the marginals of L\'evy processes, including Gaussian approximations for jumps of infinite activity. Using the convolution structure, we further derive upper bounds…

Probability · Mathematics 2018-07-17 Ester Mariucci , Markus Reiß

Recent work suggests that TCP throughput stability and predictability within a video viewing session can inform the design of better video bitrate adaptation algorithms. Despite a rich tradition of Internet measurement, however, our…

Networking and Internet Architecture · Computer Science 2015-06-19 Yi Sun , Xiaoqi Yin , Nanshu Wang , Junchen Jiang , Vyas Sekar , Yun Jin , Bruno Sinopoli

Markov chain Monte Carlo methods are central in computational statistics, and typically rely on detailed balance to ensure invariance with respect to a target distribution. Although straightforward to construct by Metropolization, this can…

Statistics Theory · Mathematics 2025-11-14 Erik Jansson , Moritz Schauer , Ruben Seyer , Akash Sharma

We consider a Markov chain on $\mathbb{R}^d$ with invariant measure $\mu$. We are interested in the rate of convergence of the empirical measures towards the invariant measure with respect to various dual distances, including in particular…

Probability · Mathematics 2022-10-13 Adrian Riekert

Consider an N-dimensional Markov chain obtained from N one-dimensional random walks by Doob h-transform with the q-Vandermonde determinant. We prove that as N becomes large, these Markov chains converge to an infinite-dimensional Feller…

Probability · Mathematics 2014-10-03 Alexei Borodin , Vadim Gorin

We are concerned with the absolute continuity of stationary distributions corresponding to some piecewise deterministic Markov process, being typically encountered in biological models. The process under investigation involves a…

Probability · Mathematics 2024-03-26 Dawid Czapla , Katarzyna Horbacz , Hanna Wojewódka-Ściążko

We introduce a unified framework to estimate the convergence of Markov chains to equilibrium in Wasserstein distance. The framework can provide convergence bounds with rates ranging from polynomial to exponential, all derived from a…

Probability · Mathematics 2025-06-09 Yanlin Qu , Jose Blanchet , Peter Glynn

We consider importance sampling as well as other properly weighted samples with respect to a target distribution $\pi$ from a different point of view. By considering the associated weights as sojourn times until the next jump, we define…

Statistics Theory · Mathematics 2007-06-13 S. Malefaki , G. Iliopoulos