scholarly journals A condition equivalent to uniform ergodicity

2005 ◽  
Vol 167 (3) ◽  
pp. 215-218
Author(s):  
Maria Elena Becker
Keyword(s):  
Uniform Ergodicity

A comparison of the ordinary and a varying parameter exponential smoothing

1989 ◽  
Vol 26 (4) ◽  
pp. 784-792 ◽  
Author(s):  
Heikki Bonsdorff
Keyword(s):  
Convergence Rate ◽  
Markov Chains ◽  
Finite Interval ◽  
Exponential Smoothing ◽  
Uniform Ergodicity ◽  
Geometric Convergence ◽  
Monotonically Increasing Function ◽  
Increasing Function

An adaptive-type exponential smoothing, motivated by an insurance tariff problem, is treated. We consider the process Zn = ß(Zn –1)Xn +(1 – ß (Zn–1))Zn–1, where Xn are i.i.d. taking values in the interval [0, M], M ≦ ∞ and ß is a monotonically increasing function [0, M] → [c, d], 0 < c < d < 1.Together with (Zn), we consider the ordinary exponential smoothing Yn = αXn + (1 – α)Yn –1 where α is a constant, 0 < α < 1. We show that (Yn) and (Zn) are geometrically ergodic Markov chains (in the case of finite interval we even have uniform ergodicity) and that EYn, EZn converge to limits EY, EZ, respectively, with a geometric convergence rate. Moreover, we show that Ez is strictly less than EY = EXn.

On the geometric ergodicity of hybrid samplers

2003 ◽  
Vol 40 (1) ◽  
pp. 123-146 ◽  
Author(s):  
G. Fort ◽  
E. Moulines ◽  
G. O. Roberts ◽  
J. S. Rosenthal
Keyword(s):  
Random Walk ◽  
Sufficient Conditions ◽  
Metropolis Algorithm ◽  
Geometric Ergodicity ◽  
Target Density ◽  
Symmetric Random Walk ◽  
Uniform Ergodicity ◽  
Random Walk Metropolis ◽  
Random Walk Metropolis Algorithm

In this paper, we consider the random-scan symmetric random walk Metropolis algorithm (RSM) on ℝd. This algorithm performs a Metropolis step on just one coordinate at a time (as opposed to the full-dimensional symmetric random walk Metropolis algorithm, which proposes a transition on all coordinates at once). We present various sufficient conditions implying V-uniform ergodicity of the RSM when the target density decreases either subexponentially or exponentially in the tails.

On the geometric ergodicity of hybrid samplers

2003 ◽  
Vol 40 (01) ◽  
pp. 123-146 ◽  
Author(s):  
G. Fort ◽  
E. Moulines ◽  
G. O. Roberts ◽  
J. S. Rosenthal
Keyword(s):  
Random Walk ◽  
Sufficient Conditions ◽  
Metropolis Algorithm ◽  
Geometric Ergodicity ◽  
Target Density ◽  
Symmetric Random Walk ◽  
Uniform Ergodicity ◽  
Random Walk Metropolis ◽  
Random Walk Metropolis Algorithm

In this paper, we consider the random-scan symmetric random walk Metropolis algorithm (RSM) on ℝ d . This algorithm performs a Metropolis step on just one coordinate at a time (as opposed to the full-dimensional symmetric random walk Metropolis algorithm, which proposes a transition on all coordinates at once). We present various sufficient conditions implying V-uniform ergodicity of the RSM when the target density decreases either subexponentially or exponentially in the tails.

scholarly journals Asymptotic Properties of a Mean-Field Model with a Continuous-State-Dependent Switching Process

2009 ◽  
Vol 46 (1) ◽  
pp. 221-243 ◽  
Author(s):  
Fubao Xi ◽  
G. Yin
Keyword(s):  
Field Model ◽  
Asymptotic Properties ◽  
Mean Field ◽  
Switching Process ◽  
Mean Field Model ◽  
State Dependent ◽  
Uniform Ergodicity ◽  
Continuous State ◽  
Feller Continuity ◽  
Drift Conditions

This work is concerned with a class of mean-field models given by a switching diffusion with a continuous-state-dependent switching process. Focusing on asymptotic properties, the regularity or nonexplosiveness, Feller continuity, and strong Feller continuity are established by means of introducing certain auxiliary processes and by making use of the truncations. Based on these results, exponential ergodicity is obtained under the Foster–Lyapunov drift conditions. By virtue of the coupling methods, the strong ergodicity or uniform ergodicity in the sense of convergence in the variation norm is established for the mean-field model with a Markovian switching process. Besides this, several examples are presented for demonstration and illustration.

V-uniform ergodicity for fluid queues

2019 ◽  
Vol 34 (1) ◽  
pp. 82-91 ◽  
Author(s):  
Yuan-yuan Liu ◽  
Yang Li
Keyword(s):  
Fluid Queues ◽  
Uniform Ergodicity

scholarly journals On the uniform ergodic for α−times integrated semigroups

2021 ◽  
Vol 39 (4) ◽  
pp. 9-20
Author(s):  
Abdelaziz Tajmouati ◽  
Abdeslam El Bakkali ◽  
Fatih Barki ◽  
Mohamed Ahmed Ould Mohamed Baba
Keyword(s):  
Integrated Semigroup ◽  
Integrated Semigroups ◽  
Uniform Ergodicity

Let $A$ be a generator of an $\alpha-$times integrated semigroup$(S(t))_{t\geq 0}$. We study the uniform ergodicity of $(S(t))_{t\geq 0}$ and we show that the range of $A$ is closed if and only if $\lambda R(\lambda,A)$ is uniformly ergodic.Moreover, we obtain that $(S(t))_{t\geq 0}$ is uniformly ergodic if and only if $\alpha=0$. Finally, we get that $\frac{1}{t^{\alpha+1}}\int_{0}^{t}S(s)ds$ converge uniformly for all $\alpha\geq 0$.

Sign in / Sign up

Export Citation Format

Share Document