scholarly journals The stability of conditional Markov processes and Markov chains in random environments

2009 ◽  
Vol 37 (5) ◽  
pp. 1876-1925 ◽  
Author(s):  
Ramon van Handel
Keyword(s):  
Markov Chains ◽  
Markov Processes ◽  
Random Environments ◽  
The Stability

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.

On determining absorption probabilities for Markov chains in random environments

1981 ◽  
Vol 13 (2) ◽  
pp. 369-387 ◽  
Author(s):  
Richard D. Bourgin ◽  
Robert Cogburn
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Random Environment ◽  
Efficient Method ◽  
General Framework ◽  
Random Environments ◽  
Extinction Probabilities ◽  
Environmental Process ◽  
Branching Chains ◽  
Absorption Probabilities

The general framework of a Markov chain in a random environment is presented and the problem of determining extinction probabilities is discussed. An efficient method for determining absorption probabilities and criteria for certain absorption are presented in the case that the environmental process is a two-state Markov chain. These results are then applied to birth and death, queueing and branching chains in random environments.

scholarly journals Probability Models for Assessing Effectiveness of Advertising Channels in the Internet Environment

2018 ◽  
pp. 209-215
Keyword(s):  
Graph Theory ◽  
Markov Chains ◽  
Markov Processes ◽  
The Internet ◽  
Probability Models ◽  
Method Of Calculation ◽  
Internet Environment ◽  
The Impact ◽  
Theory Of Graphs ◽  
Selection Of

Nowadays, marketing specialists simultaneously use several channels to attract visitors to websites. There is a difficulty in assessing not only the efficiency and conversion of each channel separately, but also in their interconnection. The problem occurs when users visit a website from several sources and only after that do the key action. To assess the effectiveness and selection of the most optimal channels, different models of attribution are used. The models are reviewed in the article. However, we propose to use multi-channel attribution, which provides an aggregate assessment of multi-channel sequences, taking into account that they are interdependent. The purpose of the paper is to create an attribution model that comprehensively evaluates multi-channel sequences and shows the effect of each channel on the conversion. The presented model of attribution can be based on the theory of graphs or Markov chains. The first method of calculation is more visual, the second (based on Markov chains) allows for work with a large amount of data. As a result, a model of multi-channel attribution was presented, which is based on Markov processes or graph theory. It allows for maximum comprehensive assessing of the impact of each channel on the conversion. On the basis of the two methods, calculations were carried out, confirming the adequacy of the model used for the tasks assigned.

scholarly journals Entropic Equilibria Selection of Stationary Extrema in Finite Populations

Entropy ◽  
2018 ◽  
Vol 20 (9) ◽  
pp. 631
Author(s):  
Marc Harper ◽  
Dashiell Fryer
Keyword(s):  
Markov Process ◽  
Population Size ◽  
Mutation Rate ◽  
Stationary Distribution ◽  
Markov Processes ◽  
Local Maxima ◽  
Moran Process ◽  
The Stability ◽  
Definition Of ◽  
Selection Of

We propose the entropy of random Markov trajectories originating and terminating at the same state as a measure of the stability of a state of a Markov process. These entropies can be computed in terms of the entropy rates and stationary distributions of Markov processes. We apply this definition of stability to local maxima and minima of the stationary distribution of the Moran process with mutation and show that variations in population size, mutation rate, and strength of selection all affect the stability of the stationary extrema.

scholarly journals Open quantum random walks, quantum Markov chains and recurrence

2019 ◽  
Vol 31 (07) ◽  
pp. 1950020 ◽  
Author(s):  
Ameur Dhahri ◽  
Farrukh Mukhamedov
Keyword(s):  
Markov Chains ◽  
Random Walks ◽  
Markov Processes ◽  
Transition Operator ◽  
Quantum Random Walks ◽  
Open Quantum ◽  
Commutative Subalgebra ◽  
Open Quantum Random Walks ◽  
Quantum Markov Chains

In the present paper, we construct QMCs (Quantum Markov Chains) associated with Open Quantum Random Walks such that the transition operator of the chain is defined by OQRW and the restriction of QMC to the commutative subalgebra coincides with the distribution [Formula: see text] of OQRW. This sheds new light on some properties of the measure [Formula: see text]. As an example, we simply mention that the measure can be considered as a distribution of some functions of certain Markov processes. Furthermore, we study several properties of QMC and associated measures. A new notion of [Formula: see text]-recurrence of QMC is studied, and the relations between the concepts of recurrence introduced in this paper and the existing ones are established.

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