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Related papers: Subgeometrically ergodic autoregressions

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A common tool in the practice of Markov Chain Monte Carlo is to use approximating transition kernels to speed up computation when the desired kernel is slow to evaluate or intractable. A limited set of quantitative tools exist to assess the…

Probability · Mathematics 2026-01-14 Jeffrey Negrea , Jeffrey S. Rosenthal

We study the convergence properties of a collapsed Gibbs sampler for Bayesian vector autoregressions with predictors, or exogenous variables. The Markov chain generated by our algorithm is shown to be geometrically ergodic regardless of…

Statistics Theory · Mathematics 2020-10-05 Karl Oskar Ekvall , Galin L. Jones

We utilize an ergodic theory framework to explore sublinear expectation theory. Specifically, we investigate the pointwise Birkhoff's ergodic theorem for invariant sublinear expectation systems. By further assuming that these sublinear…

Probability · Mathematics 2024-12-03 Wen Huang , Chunlin Liu , Shige Peng , Baoyou Qu

In the paper, we study a new rate of convergence estimate for homogeneous discrete-time nonlinear Markov chains based on the Markov-Dobrushin condition. This result generalizes the convergence estimates for any positive number of transition…

Probability · Mathematics 2021-10-22 Aleksandr A. Shchegolev

The goal of this paper is to develop a general method to establish conditional ergodicity of infinite-dimensional Markov chains. Given a Markov chain in a product space, we aim to understand the ergodic properties of its conditional…

Probability · Mathematics 2014-10-28 Xin Thomson Tong , Ramon van Handel

This paper gathers together different conditions which are all equivalent to geometric ergodicity of time-homogeneous Markov chains on general state spaces. A total of 34 different conditions are presented (27 for general chains plus 7 just…

Probability · Mathematics 2023-07-06 M. A. Gallegos-Herrada , D. Ledvinka , J. S. Rosenthal

Ergodic properties and asymptotic stationarity are investigated in this paper for the pseudo-covariance matrix (PCM) of a recursive state estimator which is robust against parametric uncertainties and is based on plant output measurements…

Systems and Control · Computer Science 2016-10-12 Tong Zhou

We propose a random adaptation variant of time-varying distributed averaging dynamics in discrete time. We show that this leads to novel interpretations of fundamental concepts in distributed averaging, opinion dynamics, and distributed…

Optimization and Control · Mathematics 2022-06-28 Rohit Parasnis , Ashwin Verma , Massimo Franceschetti , Behrouz Touri

Given pseudo-random binary sequence of length $L$, assuming it consists of $k$ sub-sequences of length $N$. We estimate how $k$ scales with growing $N$ to obtain a {\it limiting} ergodic behaviour, to fulfill the basic definition of…

Statistical Mechanics · Physics 2009-04-22 M. Süzen

We consider Gibbs samplers for a normal linear regression model with a global-local shrinkage prior and show that they produce geometrically ergodic Markov chains. First, under the horseshoe local prior and a three-parameter beta global…

Statistics Theory · Mathematics 2025-10-14 Yasuyuki Hamura

We consider a discrete time hidden Markov model where the signal is a stationary Markov chain. When conditioned on the observations, the signal is a Markov chain in a random environment under the conditional measure. It is shown that this…

Probability · Mathematics 2009-09-24 Ramon van Handel

Markov Chain Monte Carlo is repeatedly used to analyze the properties of intractable distributions in a convenient way. In this paper we derive conditions for geometric ergodicity of a general class of nonparametric stochastic volatility…

Statistical Finance · Quantitative Finance 2016-12-09 Jerzy P. Rydlewski , Małgorzata Snarska

The paper is devoted to the estimation of the rate of of exponential convergence of nonhomogeneous queues exhibiting different types of ergodicity. The main tool of our study is the method, which was proposed by the second author in the…

Probability · Mathematics 2007-06-13 Boris L. Granovsky , Aleksandr I. Zeifman

We formulate a criterion for the existence and uniqueness of an invariant measure for a Markov process taking values in a Polish phase space. In addition, weak-$^*$ ergodicity, that is, the weak convergence of the ergodic averages of the…

Probability · Mathematics 2010-10-19 Tomasz Komorowski , Szymon Peszat , Tomasz Szarek

In this article, we discuss subgeometric ergodicity of a class of regime-switching diffusion processes. We derive conditions on the drift and diffusion coefficients, and the switching mechanism which result in subgeometric ergodicity of the…

Probability · Mathematics 2022-04-12 Petra Lazić , Nikola Sandrić

This paper studies some temporal dependence properties and addresses the issue of parametric estimation for a class of state-dependent autoregressive models for nonlinear time series in which we assume a stochastic autoregressive…

Statistics Theory · Mathematics 2020-02-11 Fabio Gobbi , Sabrina Mulinacci

This paper is concerned with ergodic properties of inhomogeneous Markov processes. Since the transition probabilities depend on initial times, the existing methods to obtain invariant measures for homogeneous Markov processes are not…

Probability · Mathematics 2025-01-24 Zhenxin Liu , Di Lu

We consider the problem of defining and fitting models of autoregressive time series of probability distributions on a compact interval of $\mathbb{R}$. An order-$1$ autoregressive model in this context is to be understood as a Markov…

Methodology · Statistics 2023-03-17 Laya Ghodrati , Victor M. Panaretos

A Markov chain is geometrically ergodic if it converges to its in- variant distribution at a geometric rate in total variation norm. We study geo- metric ergodicity of deterministic and random scan versions of the two-variable Gibbs…

Statistics Theory · Mathematics 2012-06-22 Aixin Tan , Galin L. Jones , James P. Hobert

We develop a general framework for studying ergodicity of order-preserving Markov semigroups. We establish natural and in a certain sense optimal conditions for existence and uniqueness of the invariant measure and exponential convergence…

Probability · Mathematics 2020-10-28 Oleg Butkovsky , Michael Scheutzow