scholarly journals Subgeometric Ergodicity under Random-Time State-Dependent Drift Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Mokaedi V. Lekgari
Keyword(s):  
Markov Chains ◽  
Stochastic Networks ◽  
Random Time ◽  
Stopping Times ◽  
Lyapunov Techniques ◽  
State Dependent ◽  
Drift Conditions ◽  
The Stability

Motivated by possible applications of Lyapunov techniques in the stability of stochastic networks, subgeometric ergodicity of Markov chains is investigated. In a nutshell, in this study we take a look atf-ergodic general Markov chains, subgeometrically ergodic at rater, when the random-time Foster-Lyapunov drift conditions on a set of stopping times are satisfied.

scholarly journals Subgeometric Ergodicity Analysis of Continuous-Time Markov Chains under Random-Time State-Dependent Lyapunov Drift Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Mokaedi V. Lekgari
Keyword(s):  
Markov Chains ◽  
Discrete Time ◽  
Continuous Time ◽  
Random Time ◽  
Lyapunov Analysis ◽  
Continuous Time Markov Chains ◽  
State Dependent ◽  
Drift Conditions

We investigate random-time state-dependent Foster-Lyapunov analysis on subgeometric rate ergodicity of continuous-time Markov chains (CTMCs). We are mainly concerned with making use of the available results on deterministic state-dependent drift conditions for CTMCs and on random-time state-dependent drift conditions for discrete-time Markov chains and transferring them to CTMCs.

scholarly journals Maximal Coupling Procedure and Stability of Continuous-Time Markov Chains

2014 ◽  
Vol 10 ◽  
pp. 30-37
Author(s):  
Mokaedi V. Lekgari
Keyword(s):  
Markov Chains ◽  
Markov Processes ◽  
Continuous Time ◽  
Stopping Times ◽  
Continuous Time Markov Chains ◽  
Maximal Coupling ◽  
Countable State ◽  
Coupling Procedure ◽  
The Stability

In this study we first investigate the stability of subsampled discrete Markov chains through the use of the maximal coupling procedure. This is an extension of the available results on Markov chains and is realized through the analysis of the subsampled chain ΦΤn, where {Τn, nєZ+}is an increasing sequence of random stopping times. Then the similar results are realized for the stability of countable-state Continuous-time Markov processes by employing the skeleton-chain method.

scholarly journals Foster-type criteria for Markov chains on general spaces

2006 ◽  
Vol 43 (4) ◽  
pp. 1194-1200 ◽  
Author(s):  
Brian H. Fralix
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
State Space ◽  
Open Problem ◽  
Stopping Times ◽  
Geometric Ergodicity ◽  
General State ◽  
Harris Recurrence ◽  
General State Space ◽  
Drift Conditions

This paper establishes new Foster-type criteria for a Markov chain on a general state space to be Harris recurrent, positive Harris recurrent, or geometrically ergodic. The criteria are based on drift conditions involving stopping times rather than deterministic steps. Meyn and Tweedie (1994) developed similar criteria involving random-sized steps, independent of the Markov chain under study. They also posed an open problem of finding criteria involving stopping times. Our results essentially solve that problem. We also show that the assumption of ψ-irreducibility is not needed when stating our drift conditions for positive Harris recurrence or geometric ergodicity.

scholarly journals Foster-type criteria for Markov chains on general spaces

2006 ◽  
Vol 43 (04) ◽  
pp. 1194-1200 ◽  
Author(s):  
Brian H. Fralix
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
State Space ◽  
Open Problem ◽  
Stopping Times ◽  
Geometric Ergodicity ◽  
General State ◽  
Harris Recurrence ◽  
General State Space ◽  
Drift Conditions

This paper establishes new Foster-type criteria for a Markov chain on a general state space to be Harris recurrent, positive Harris recurrent, or geometrically ergodic. The criteria are based on drift conditions involving stopping times rather than deterministic steps. Meyn and Tweedie (1994) developed similar criteria involving random-sized steps, independent of the Markov chain under study. They also posed an open problem of finding criteria involving stopping times. Our results essentially solve that problem. We also show that the assumption of ψ-irreducibility is not needed when stating our drift conditions for positive Harris recurrence or geometric ergodicity.

Stabilization of networked switched affine systems with event-triggered strategy

2021 ◽  
pp. 014233122110213
Author(s):  
Dandan Li ◽  
Zhiqiang Zuo ◽  
Yijing Wang
Keyword(s):  
Affine Systems ◽  
Switching Law ◽  
Event Time ◽  
Sliding Motion ◽  
State Dependent ◽  
Event Triggering ◽  
Stability Issue ◽  
The Stability ◽  
Event Based ◽  
Selection Of

Using an event-based switching law, we address the stability issue for continuous-time switched affine systems in the network environment. The state-dependent switching law in terms of the region function is firstly developed. We combine the region function with the event-triggering mechanism to construct the switching law. This can provide more candidates for the selection of the next activated subsystem at each switching instant. As a result, it is possible for us to activate the appropriate subsystem to avoid the sliding motion. The Zeno behavior for the switched affine system can be naturally ruled out by guaranteeing a positive minimum inter-event time between two consecutive executions of the event-triggering threshold. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed method.

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