The stability of Markov chains with partially equicontinuous transition structure

2016 ◽  
Author(s):  
Dawid Czapla ◽  
Katarzyna Horbacz
Keyword(s):  
Markov Chains ◽  
Transition Structure ◽  
The Stability

Conditions for the non-ergodicity of Markov chains with application to a communication system

1987 ◽  
Vol 24 (2) ◽  
pp. 339-346 ◽  
Author(s):  
Linn I. Sennott
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Communication System ◽  
System Performance ◽  
Multiple Access ◽  
Sufficient Condition ◽  
Performance Bounds ◽  
Communication System Performance ◽  
Null Recurrence ◽  
The Stability

We obtain a sufficient condition for the transience of a Markov chain, and a sufficient condition for its null recurrence. These are applied to characterize the stability of a multiple-access communication system. Performance bounds for the system are also obtained.

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.

Observing Customer Segment Stability Using Soft Computing Techniques and Markov Chains Within Data Mining Framework

2018 ◽  
pp. 1440-1457
Author(s):  
Abdulkadir Hiziroglu
Keyword(s):  
Data Mining ◽  
Markov Chains ◽  
Soft Computing ◽  
Internal Validity ◽  
Real World Data ◽  
Soft Computing Techniques ◽  
Customer Segment ◽  
Managerial Implications ◽  
Classification Prediction ◽  
The Stability

This study proposes a model that utilizes soft computing and Markov Chains within a data mining framework to observe the stability of customer segments. The segmentation process in this study includes clustering of existing consumers and classification-prediction of segments for existing and new customers. Both a combination and an integration of soft computing techniques were used in the proposed model. Segmenting customers was done according to the purchasing behaviours of customers based on RFM (Recency, Frequency, Monetary) values. The model was applied to real-world data that were procured from a UK retail chain covering four periods of shopping transactions of around 300,000 customers. Internal validity was measured by two different clustering validity indices and a classification accuracy test. Some meaningful information associated with segment stability was extracted to provide practitioners a better understanding of segment stability over time and useful managerial implications.

scholarly journals Regular Perturbation of V-Geometrically Ergodic Markov Chains

2013 ◽  
Vol 50 (01) ◽  
pp. 184-194 ◽  
Author(s):  
Déborah Ferré ◽  
Loïc Hervé ◽  
James Ledoux
Keyword(s):  
Perturbation Theory ◽  
Asymptotic Expansion ◽  
Probability Density Function ◽  
Markov Chains ◽  
Invariant Probability Measure ◽  
Regular Perturbation ◽  
Regularity Properties ◽  
The Stability ◽  
Higher Regularity ◽  
Standard Perturbation Theory

In this paper, new conditions for the stability ofV-geometrically ergodic Markov chains are introduced. The results are based on an extension of the standard perturbation theory formulated by Keller and Liverani. The continuity and higher regularity properties are investigated. As an illustration, an asymptotic expansion of the invariant probability measure for an autoregressive model with independent and identically distributed noises (with a nonstandard probability density function) is obtained.

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