Modelling: Markov Chains and Markov Processes

1998 ◽  
pp. 41-88
Author(s):  
Charles S. Tapiero
Keyword(s):  
Markov Chains ◽  
Markov Processes

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 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.

scholarly journals Limit Theorems for Semi-Markov Processes and Renewal Theory for Markov Chains

1978 ◽  
Vol 6 (5) ◽  
pp. 788-797 ◽  
Author(s):  
K. B. Athreya ◽  
D. McDonald ◽  
P. Ney
Keyword(s):  
Markov Chains ◽  
Markov Processes ◽  
Limit Theorems ◽  
Renewal Theory ◽  
Semi Markov Processes

On fluctuation problems in the theory of queues

1976 ◽  
Vol 8 (03) ◽  
pp. 548-583 ◽  
Author(s):  
Lajos Takács
Keyword(s):  
Markov Chains ◽  
Markov Processes ◽  
Generating Functions ◽  
Finite Differences ◽  
Historical Development ◽  
Banach Algebras ◽  
Point Of View ◽  
Mathematical Methods ◽  
Operator Calculus ◽  
Complex Functions

This paper gives a survey of the historical development of the solutions of various fluctuation problems in the theory of queues from the point of view of the mathematical methods used. These methods include Markov chains, Markov processes, integral equations, complex functions, generating functions, Laplace transforms, factorization of functions, operator calculus, Banach algebras and some particular methods, such as calculus of finite differences and combinatorics. In addition, the paper contains several recent results of the author for semi-Markov queuing processes.

Markov processes for modeling and analyzing a new genetic mapping method

1993 ◽  
Vol 30 (04) ◽  
pp. 766-779 ◽  
Author(s):  
Eleanor Feingold
Keyword(s):  
Markov Chains ◽  
Genetic Mapping ◽  
Stochastic Processes ◽  
Markov Processes ◽  
Mapping Method ◽  
Central Issue ◽  
Boundary Crossing ◽  
Crossing Probabilities

This paper describes a set of stochastic processes that is useful for modeling and analyzing a new genetic mapping method. Some of the processes are Markov chains, and some are best described as functions of Markov chains. The central issue is boundary-crossing probabilities, which correspond to p-values for the existence of genes for particular traits. The methods elaborated by Aldous (1989) provide very accurate approximate p-values, as spot-checked against simulations.

scholarly journals MARKOV STATES AND CHAINS ON THE CAR ALGEBRA

2007 ◽  
Vol 10 (02) ◽  
pp. 165-183 ◽  
Author(s):  
LUIGI ACCARDI ◽  
FRANCESCO FIDALEO ◽  
FARRUH MUKHAMEDOV
Keyword(s):  
Markov Chains ◽  
Tensor Product ◽  
Markov Processes ◽  
Car Algebra ◽  
Quantum Markov Processes ◽  
Canonical Anticommutation Relations ◽  
Satisfactory Theory ◽  
Quantum Markov Chains ◽  
General Method

We introduce the notion of Markov states and chains on the Canonical Anticommutation Relations algebra over ℤ, emphasizing some remarkable differences with the infinite tensor product case. We describe the structure of the Markov states on this algebra and show that, contrarily to the infinite tensor product case, not all these states are diagonalizable. A general method to construct nontrivial quantum Markov chains on the CAR algebra is also proposed and illustrated by some pivotal examples. This analysis provides a further step for a satisfactory theory of quantum Markov processes.

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.

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