Some properties of quasi-stationary distributions for finite Markov chains

2011 ◽  
pp. 59-66
Author(s):  
Servet Martínez ◽  
Jaime San Martín
Keyword(s):  
Markov Chains ◽  
Stationary Distributions ◽  
Finite Markov Chains

On quasi-stationary distributions in absorbing continuous-time finite Markov chains

1967 ◽  
Vol 4 (1) ◽  
pp. 192-196 ◽  
Author(s):  
J. N. Darroch ◽  
E. Seneta
Keyword(s):  
Markov Chains ◽  
Discrete Time ◽  
Continuous Time ◽  
Present Note ◽  
Time Parameter ◽  
Stationary Distributions ◽  
Finite State ◽  
Absorbing Markov Chains ◽  
Finite Markov Chains ◽  
Finite State Space

In a recent paper, the authors have discussed the concept of quasi-stationary distributions for absorbing Markov chains having a finite state space, with the further restriction of discrete time. The purpose of the present note is to summarize the analogous results when the time parameter is continuous.

On Quasi-Stationary distributions in absorbing discrete-time finite Markov chains

1965 ◽  
Vol 2 (1) ◽  
pp. 88-100 ◽  
Author(s):  
J. N. Darroch ◽  
E. Seneta
Keyword(s):  
Markov Chain ◽  
Probability Distribution ◽  
Markov Chains ◽  
Stationary Distribution ◽  
Discrete Time ◽  
Stationary Distributions ◽  
Transient States ◽  
Reverse Process ◽  
Finite Markov Chains ◽  
Quasi Stationary Distribution

The time to absorption from the set T of transient states of a Markov chain may be sufficiently long for the probability distribution over T to settle down in some sense to a “quasi-stationary” distribution. Various analogues of the stationary distribution of an irreducible chain are suggested and compared. The reverse process of an absorbing chain is found to be relevant.

On Quasi-Stationary distributions in absorbing discrete-time finite Markov chains

1965 ◽  
Vol 2 (01) ◽  
pp. 88-100 ◽  
Author(s):  
J. N. Darroch ◽  
E. Seneta
Keyword(s):  
Markov Chain ◽  
Probability Distribution ◽  
Markov Chains ◽  
Stationary Distribution ◽  
Discrete Time ◽  
Stationary Distributions ◽  
Transient States ◽  
Reverse Process ◽  
Finite Markov Chains ◽  
Quasi Stationary Distribution

The time to absorption from the set T of transient states of a Markov chain may be sufficiently long for the probability distribution over T to settle down in some sense to a “quasi-stationary” distribution. Various analogues of the stationary distribution of an irreducible chain are suggested and compared. The reverse process of an absorbing chain is found to be relevant.

On quasi-stationary distributions in absorbing continuous-time finite Markov chains

1967 ◽  
Vol 4 (01) ◽  
pp. 192-196 ◽  
Author(s):  
J. N. Darroch ◽  
E. Seneta
Keyword(s):  
Markov Chains ◽  
Discrete Time ◽  
Continuous Time ◽  
Present Note ◽  
Time Parameter ◽  
Stationary Distributions ◽  
Finite State ◽  
Absorbing Markov Chains ◽  
Finite Markov Chains ◽  
Finite State Space

In a recent paper, the authors have discussed the concept of quasi-stationary distributions for absorbing Markov chains having a finite state space, with the further restriction of discrete time. The purpose of the present note is to summarize the analogous results when the time parameter is continuous.

scholarly journals Intersection Conductance and Canonical Alternating Paths: Methods for General Finite Markov Chains

2014 ◽  
Vol 23 (4) ◽  
pp. 585-606
Author(s):  
RAVI MONTENEGRO
Keyword(s):  
Markov Chains ◽  
Cayley Graph ◽  
Mixing Time ◽  
Symmetric Case ◽  
Generating Set ◽  
Finite Markov Chains

We extend the conductance and canonical paths methods to the setting of general finite Markov chains, including non-reversible non-lazy walks. The new path method is used to show that a known bound for the mixing time of a lazy walk on a Cayley graph with a symmetric generating set also applies to the non-lazy non-symmetric case, often even when there is no holding probability.

A representation theorem for finite Markov chains whose states are subintervals of [0, 1]

1971 ◽  
Vol 3 (1) ◽  
pp. 51-58 ◽  
Author(s):  
S. Sankar Sengupta ◽  
P. Czarny ◽  
Ray Chow
Keyword(s):  
Markov Chains ◽  
Representation Theorem ◽  
Finite Markov Chains

Perturbation theory and finite Markov chains

1968 ◽  
Vol 5 (2) ◽  
pp. 401-413 ◽  
Author(s):  
Paul J. Schweitzer
Keyword(s):  
Perturbation Theory ◽  
Markov Chain ◽  
Markov Chains ◽  
Stationary Distribution ◽  
Fundamental Matrix ◽  
Transition Probabilities ◽  
Semi Group ◽  
Partial Derivatives ◽  
Finite Markov Chains ◽  
Derivatives Of

A perturbation formalism is presented which shows how the stationary distribution and fundamental matrix of a Markov chain containing a single irreducible set of states change as the transition probabilities vary. Expressions are given for the partial derivatives of the stationary distribution and fundamental matrix with respect to the transition probabilities. Semi-group properties of the generators of transformations from one Markov chain to another are investigated. It is shown that a perturbation formalism exists in the multiple subchain case if and only if the change in the transition probabilities does not alter the number of, or intermix the various subchains. The formalism is presented when this condition is satisfied.

scholarly journals Analytic-geometric methods for finite Markov chains with applications to quasi-stationarity

2020 ◽  
Vol 17 (2) ◽  
pp. 901
Author(s):  
Persi Diaconis ◽  
Kelsey Houston-Edwards ◽  
Laurent Saloff-Coste
Keyword(s):  
Markov Chains ◽  
Geometric Methods ◽  
Finite Markov Chains
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