Connecting reversible Markov processes

1986 ◽  
Vol 18 (4) ◽  
pp. 880-900 ◽  
Author(s):  
P. K. Pollett
Keyword(s):  
Invariant Measure ◽  
Random Walks ◽  
Markov Processes ◽  
Product Form ◽  
Migration Process ◽  
Reversible Markov Processes

We provide a framework for interconnecting a collection of reversible Markov processes in such a way that the resulting process has a product-form invariant measure with respect to which the process is reversible. A number of examples are discussed including Kingman&s reversible migration process, interconnected random walks and stratified clustering processes.

Connecting reversible Markov processes

1986 ◽  
Vol 18 (04) ◽  
pp. 880-900 ◽  
Author(s):  
P. K. Pollett
Keyword(s):  
Invariant Measure ◽  
Random Walks ◽  
Markov Processes ◽  
Product Form ◽  
Migration Process ◽  
Reversible Markov Processes

We provide a framework for interconnecting a collection of reversible Markov processes in such a way that the resulting process has a product-form invariant measure with respect to which the process is reversible. A number of examples are discussed including Kingman&s reversible migration process, interconnected random walks and stratified clustering processes.

Connecting internally balanced quasi-reversible Markov processes

1992 ◽  
Vol 24 (04) ◽  
pp. 934-959 ◽  
Author(s):  
W. Henderson ◽  
C. E. M. Pearce ◽  
P. K. Pollett ◽  
P. G. Taylor
Keyword(s):  
Invariant Measure ◽  
Markov Processes ◽  
General Framework ◽  
Feedback Mechanism ◽  
Product Form ◽  
Reversible Markov Processes ◽  
The Individual ◽  
Internal Balance ◽  
Feedback Queues ◽  
Individual Nodes

We provide a general framework for interconnecting a collection of quasi-reversible nodes in such a way that the resulting process exhibits a product-form invariant measure. The individual nodes can be quite general, although some degree of internal balance will be assumed. Any of the nodes may possess a feedback mechanism. Indeed, we pay particular attention to a class of feedback queues, characterized by the fact that their state description allows one to maintain a record of the order in which events occur. We also examine in some detail the problem of determining for which values of the arrival rates a node does exhibit quasi-reversibility.

Connecting internally balanced quasi-reversible Markov processes

1992 ◽  
Vol 24 (4) ◽  
pp. 934-959 ◽  
Author(s):  
W. Henderson ◽  
C. E. M. Pearce ◽  
P. K. Pollett ◽  
P. G. Taylor
Keyword(s):  
Invariant Measure ◽  
Markov Processes ◽  
General Framework ◽  
Feedback Mechanism ◽  
Product Form ◽  
Reversible Markov Processes ◽  
The Individual ◽  
Internal Balance ◽  
Feedback Queues ◽  
Individual Nodes

We provide a general framework for interconnecting a collection of quasi-reversible nodes in such a way that the resulting process exhibits a product-form invariant measure. The individual nodes can be quite general, although some degree of internal balance will be assumed. Any of the nodes may possess a feedback mechanism. Indeed, we pay particular attention to a class of feedback queues, characterized by the fact that their state description allows one to maintain a record of the order in which events occur. We also examine in some detail the problem of determining for which values of the arrival rates a node does exhibit quasi-reversibility.

Coherent random walks arising in some genetical models

1976 ◽  
Vol 351 (1664) ◽  
pp. 19-31 ◽  
Keyword(s):  
Population Genetics ◽  
Random Walks ◽  
Markov Processes ◽  
Stochastic Models ◽  
Equilibrium Distribution ◽  
Large Sample ◽  
Random Variation

Certain stochastic models used in population genetics have the form of Markov processes in which a group of N points moves randomly on a line, and in which an equilibrium distribution exists for the relative configura­tion of the group. The properties of this equilibrium are studied, with particular reference to a certain limiting situation as N becomes large. In this limit the group of points is distributed like a large sample from a distribution which is itself subject to random variation.

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 Reversible Markov Processes

1973 ◽  
Vol 1 (6) ◽  
pp. 1014-1025
Author(s):  
Michael L. Levitan ◽  
Lawrence H. Smolowitz
Keyword(s):  
Markov Processes ◽  
Limit Theorems ◽  
Reversible Markov Processes

An operation which inverts Bernoulli multiplication and associated stationary reversible Markov processes

1992 ◽  
Vol 29 (01) ◽  
pp. 234-238 ◽  
Author(s):  
R. P. Littlejohn
Keyword(s):  
Time Series ◽  
Markov Processes ◽  
Marginal Distribution ◽  
Ovulation Rate ◽  
Simple Operation ◽  
Reversible Markov Processes

A simple operation is described which inverts Bernoulli multiplication. It is used to define two classes of stationary reversible Markov processes with general marginal distribution. These are compared to the DAR(1) process of Jacobs and Lewis (1978). LJAR(1) is used to model ovulation rate time series.

Online Network Optimization Using Product-Form Markov Processes

2016 ◽  
Vol 61 (7) ◽  
pp. 1838-1853 ◽  
Author(s):  
Jaron Sanders ◽  
Sem C. Borst ◽  
Johan S. H. van Leeuwaarden
Keyword(s):  
Markov Processes ◽  
Network Optimization ◽  
Product Form
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