scholarly journals Fuzzy Eigenvalues and Fuzzy Eigenvectors of Fuzzy Markov Chain Transition Matrix under Max-min Composition

2015 ◽  
Vol 2015 (1) ◽  
pp. 25-35 ◽  
Author(s):  
Jean Pierre Mukeba Kanyinda ◽  
Rostin Mabela Makengo Matendo ◽  
Berthold Ulungu Ekunda Lukata ◽  
Donatien Ntantu Ibula
Keyword(s):  
Markov Chain ◽  
Transition Matrix ◽  
Fuzzy Markov Chain ◽  
Fuzzy Eigenvalues

Truncation approximations of invariant measures for Markov chains

1998 ◽  
Vol 35 (03) ◽  
pp. 517-536 ◽  
Author(s):  
R. L. Tweedie
Keyword(s):  
Markov Chain ◽  
Probability Distribution ◽  
Markov Chains ◽  
Transition Matrix ◽  
Invariant Measures ◽  
Invariant Distribution ◽  
Special Cases ◽  
Recurrent Markov Chain ◽  
Positive Recurrent

Let P be the transition matrix of a positive recurrent Markov chain on the integers, with invariant distribution π. If (n) P denotes the n x n ‘northwest truncation’ of P, it is known that approximations to π(j)/π(0) can be constructed from (n) P, but these are known to converge to the probability distribution itself in special cases only. We show that such convergence always occurs for three further general classes of chains, geometrically ergodic chains, stochastically monotone chains, and those dominated by stochastically monotone chains. We show that all ‘finite’ perturbations of stochastically monotone chains can be considered to be dominated by such chains, and thus the results hold for a much wider class than is first apparent. In the cases of uniformly ergodic chains, and chains dominated by irreducible stochastically monotone chains, we find practical bounds on the accuracy of the approximations.

Non-stationary fuzzy Markov chain

2007 ◽  
Vol 28 (16) ◽  
pp. 2201-2208 ◽  
Author(s):  
F. Salzenstein ◽  
C. Collet ◽  
S. Lecam ◽  
M. Hatt
Keyword(s):  
Markov Chain ◽  
Fuzzy Markov Chain

Determining Equivalent Resistance and Nodal Potentials of a Resistive Circuit Using a Reduced Transition Matrix

2020 ◽  
Vol 02 (01) ◽  
pp. 2050004
Author(s):  
Je-Young Choi
Keyword(s):  
Markov Chain ◽  
Random Walk ◽  
Random Walks ◽  
Transition Matrix ◽  
Present Approach ◽  
Voltage Source ◽  
Equivalent Resistance ◽  
Electrical Circuits ◽  
Electric Potentials ◽  
Dominant Eigenvector

Several methods have been developed in order to solve electrical circuits consisting of resistors and an ideal voltage source. A correspondence with random walks avoids difficulties caused by choosing directions of currents and signs in potential differences. Starting from the random-walk method, we introduce a reduced transition matrix of the associated Markov chain whose dominant eigenvector alone determines the electric potentials at all nodes of the circuit and the equivalent resistance between the nodes connected to the terminals of the voltage source. Various means to find the eigenvector are developed from its definition. A few example circuits are solved in order to show the usefulness of the present approach.

scholarly journals A note on repeated sequences in Markov chains

1987 ◽  
Vol 19 (03) ◽  
pp. 739-742 ◽  
Author(s):  
J. D. Biggins
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Renewal Process ◽  
Transition Matrix ◽  
Repeated Sequences ◽  
Markov Renewal Process ◽  
Conditional Mean ◽  
Sojourn Times

If (non-overlapping) repeats of specified sequences of states in a Markov chain are considered, the result is a Markov renewal process. Formulae somewhat simpler than those given in Biggins and Cannings (1987) are derived which can be used to obtain the transition matrix and conditional mean sojourn times in this process.

scholarly journals Looking Forwards and Backwards in the Multi-Allelic Neutral Cannings Population Model

2010 ◽  
Vol 47 (03) ◽  
pp. 713-731 ◽  
Author(s):  
M. Möhle
Keyword(s):  
Markov Chain ◽  
Population Size ◽  
Side Effect ◽  
Population Model ◽  
Inversion Formula ◽  
Transition Matrix ◽  
Duality Relation ◽  
Moran Model ◽  
Fisher Model ◽  
Fixed Population

We look forwards and backwards in the multi-allelic neutral exchangeable Cannings model with fixed population size and nonoverlapping generations. The Markov chain X is studied which describes the allelic composition of the population forward in time. A duality relation (inversion formula) between the transition matrix of X and an appropriate backward matrix is discussed. The probabilities of the backward matrix are explicitly expressed in terms of the offspring distribution, complementing the work of Gladstien (1978). The results are applied to fundamental multi-allelic Cannings models, among them the Moran model, the Wright-Fisher model, the Kimura model, and the Karlin and McGregor model. As a side effect, number theoretical sieve formulae occur in these examples.

Monotonicity results for MR/GI/1 queues

1997 ◽  
Vol 34 (02) ◽  
pp. 514-524 ◽  
Author(s):  
Nicole Bäuerle
Keyword(s):  
Markov Chain ◽  
Waiting Time ◽  
Transition Matrix ◽  
Stochastic Ordering ◽  
Arrival Process ◽  
Stationary Waiting Time ◽  
Monotonicity Results

This paper considers queues with a Markov renewal arrival process and a particular transition matrix for the underlying Markov chain. We study the effect that the transition matrix has on the waiting time of the nth customer as well as on the stationary waiting time. The main theorem generalizes results of Szekli et al. (1994a) and partly confirms their conjecture. In this context we show the importance of a new stochastic ordering concept.

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