On the rate of convergence in von Neumann's ergodic theorem with continuous time

2010 ◽  
Vol 201 (4) ◽  
pp. 493-500 ◽  
Author(s):  
A G Kachurovskii ◽  
Anna V Reshetenko
Keyword(s):  
Rate Of Convergence ◽  
Ergodic Theorem ◽  
Continuous Time ◽  
Von Neumann’S Ergodic Theorem

scholarly journals Noncommutative weighted individual ergodic theorems with continuous time

2020 ◽  
Vol 23 (02) ◽  
pp. 2050013
Author(s):  
Vladimir Chilin ◽  
Semyon Litvinov
Keyword(s):  
Ergodic Theorem ◽  
Continuous Time ◽  
Symmetric Spaces ◽  
Von Neumann Algebra ◽  
Ergodic Theorems ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Von Neumann ◽  
Marcinkiewicz Spaces ◽  
Local Ergodic Theorem

We show that ergodic flows in the noncommutative [Formula: see text]-space (associated with a semifinite von Neumann algebra) generated by continuous semigroups of positive Dunford–Schwartz operators and modulated by bounded Besicovitch almost periodic functions converge almost uniformly. The corresponding local ergodic theorem is also proved. We then extend these results to arbitrary noncommutative fully symmetric spaces and present applications to noncommutative Orlicz (in particular, noncommutative [Formula: see text]-spaces), Lorentz, and Marcinkiewicz spaces. The commutative counterparts of the results are derived.

On Sharp Bounds on the Rate of Convergence for Finite Continuous-Time Markovian Queueing Models

2018 ◽  
pp. 20-28 ◽  
Author(s):  
Alexander Zeifman ◽  
Alexander Sipin ◽  
Victor Korolev ◽  
Galina Shilova ◽  
Ksenia Kiseleva ◽  
...  
Keyword(s):  
Rate Of Convergence ◽  
Continuous Time ◽  
Queueing Models ◽  
Sharp Bounds

Stability and exponential convergence of continuous-time Markov chains

2003 ◽  
Vol 40 (04) ◽  
pp. 970-979 ◽  
Author(s):  
A. Yu. Mitrophanov
Keyword(s):  
Markov Chains ◽  
Rate Of Convergence ◽  
Stationary Distribution ◽  
Continuous Time ◽  
Exponential Convergence ◽  
Perturbation Bounds ◽  
Continuous Time Markov Chains ◽  
The Relationship

For finite, homogeneous, continuous-time Markov chains having a unique stationary distribution, we derive perturbation bounds which demonstrate the connection between the sensitivity to perturbations and the rate of exponential convergence to stationarity. Our perturbation bounds substantially improve upon the known results. We also discuss convergence bounds for chains with diagonalizable generators and investigate the relationship between the rate of convergence and the sensitivity of the eigenvalues of the generator; special attention is given to reversible chains.

Conditions for strong ergodicity using intensity matrices

1988 ◽  
Vol 25 (1) ◽  
pp. 34-42 ◽  
Author(s):  
Jean Johnson ◽  
Dean Isaacson
Keyword(s):  
Markov Chains ◽  
Rate Of Convergence ◽  
Discrete Time ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Limiting Behavior ◽  
Strong Ergodicity ◽  
Continuous Time Markov Chains

Sufficient conditions for strong ergodicity of discrete-time non-homogeneous Markov chains have been given in several papers. Conditions have been given using the left eigenvectors ψn of Pn(ψ nPn = ψ n) and also using the limiting behavior of Pn. In this paper we consider the analogous results in the case of continuous-time Markov chains where one uses the intensity matrices Q(t) instead of P(s, t). A bound on the rate of convergence of certain strongly ergodic chains is also given.

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