Moments for stationary and quasi-stationary distributions of markov chains

1985 ◽  
Vol 22 (1) ◽  
pp. 148-155 ◽  
Author(s):  
E. Seneta ◽  
R. L. Tweedie
Keyword(s):  
Invariant Measure ◽  
Markov Chains ◽  
Stationary Distributions ◽  
Limit Distributions ◽  
Sufficient Set ◽  
Watson Process ◽  
Necessary And Sufficient ◽  
Conditional Limit ◽  
Finite Moments

A necessary and sufficient set of conditions is given for the finiteness of a general moment of the R -invariant measure of an R -recurrent substochastic matrix. The conditions are conceptually related to Foster's theorem. The result extends that of [8], and is illustratively applied to the single and multitype subcritical Galton–Watson process to find conditions for Yaglom-type conditional limit distributions to have finite moments.

Moments for stationary and quasi-stationary distributions of markov chains

1985 ◽  
Vol 22 (01) ◽  
pp. 148-155 ◽  
Author(s):  
E. Seneta ◽  
R. L. Tweedie
Keyword(s):  
Invariant Measure ◽  
Markov Chains ◽  
Stationary Distributions ◽  
Limit Distributions ◽  
Sufficient Set ◽  
Watson Process ◽  
Necessary And Sufficient ◽  
Conditional Limit ◽  
Finite Moments

A necessary and sufficient set of conditions is given for the finiteness of a general moment of the R -invariant measure of an R -recurrent substochastic matrix. The conditions are conceptually related to Foster's theorem. The result extends that of [8], and is illustratively applied to the single and multitype subcritical Galton–Watson process to find conditions for Yaglom-type conditional limit distributions to have finite moments.

Quasi-stationary distributions for Markov chains on a general state space

1974 ◽  
Vol 11 (4) ◽  
pp. 726-741 ◽  
Author(s):  
Richard. L. Tweedie
Keyword(s):  
Markov Chain ◽  
Invariant Measure ◽  
Markov Chains ◽  
State Space ◽  
Finiteness Condition ◽  
General State ◽  
Stationary Distributions ◽  
General State Space ◽  
Countably Infinite ◽  
Stationary Behaviour

The quasi-stationary behaviour of a Markov chain which is φ-irreducible when restricted to a subspace of a general state space is investigated. It is shown that previous work on the case where the subspace is finite or countably infinite can be extended to general chains, and the existence of certain quasi-stationary limits as honest distributions is equivalent to the restricted chain being R-positive with the unique R-invariant measure satisfying a certain finiteness condition.

On the existence of submultiplicative moments for the stationary distributions of some Markovian random walks

1999 ◽  
Vol 36 (1) ◽  
pp. 78-85 ◽  
Author(s):  
M. S. Sgibnev
Keyword(s):  
Markov Chains ◽  
Random Walks ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Necessary And Sufficient Conditions ◽  
Stationary Distributions ◽  
Necessary And Sufficient ◽  
Submultiplicative Function ◽  
Independent Identically Distributed

This paper is concerned with submultiplicative moments for the stationary distributions π of some Markov chains taking values in ℝ+ or ℝ which are closely related to the random walks generated by sequences of independent identically distributed random variables. Necessary and sufficient conditions are given for ∫φ(x)π(dx) < ∞, where φ(x) is a submultiplicative function, i.e. φ(0) = 1 and φ(x+y) ≤ φ(x)φ(y) for all x, y.

On the Problem of Establishing the Existence of Stationary Distributions for Continuous-Time Markov Chains

1993 ◽  
Vol 7 (4) ◽  
pp. 529-543 ◽  
Author(s):  
P. K. Pollett ◽  
P. G. Taylor
Keyword(s):  
Markov Chains ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Sufficient Condition ◽  
Transition Rates ◽  
Necessary And Sufficient Condition ◽  
Stationary Distributions ◽  
Continuous Time Markov Chains ◽  
Necessary And Sufficient ◽  
Networks Of Queues

We consider the problem of establishing the existence of stationary distributions for continuous-time Markov chains directly from the transition rates Q. Given an invariant probability distribution m for Q, we show that a necessary and sufficient condition for m to be a stationary distribution for the minimal process is that Q be regular. We provide sufficient conditions for the regularity of Q that are simple to verify in practice, thus allowing one to easily identify stationary distributions for a variety of models. To illustrate our results, we shall consider three classes of multidimensional Markov chains, namely, networks of queues with batch movements, semireversible queues, and partially balanced Markov processes.

On a result of Rubin and Vere-Jones concerning subcritical branching processes

1976 ◽  
Vol 13 (04) ◽  
pp. 804-808
Author(s):  
Fred M. Hoppe
Keyword(s):  
Mass Distribution ◽  
Generating Function ◽  
Branching Processes ◽  
Probability Generating Function ◽  
Single Parameter ◽  
Limit Distributions ◽  
Arbitrary Mass ◽  
One To One ◽  
Watson Process ◽  
Conditional Limit

If a subcritical Galton-Watson process is initiated with an arbitrary mass distribution, then it is known that under certain conditions proper conditional limit distributions exist, depending on a single parameter. It is shown here that there is a one-to-one correspondence between these distributions and those arising from the process with a linear offspring probability generating function.

On a result of Rubin and Vere-Jones concerning subcritical branching processes

1976 ◽  
Vol 13 (4) ◽  
pp. 804-808 ◽  
Author(s):  
Fred M. Hoppe
Keyword(s):  
Mass Distribution ◽  
Generating Function ◽  
Branching Processes ◽  
Probability Generating Function ◽  
Single Parameter ◽  
Limit Distributions ◽  
Arbitrary Mass ◽  
One To One ◽  
Watson Process ◽  
Conditional Limit

If a subcritical Galton-Watson process is initiated with an arbitrary mass distribution, then it is known that under certain conditions proper conditional limit distributions exist, depending on a single parameter. It is shown here that there is a one-to-one correspondence between these distributions and those arising from the process with a linear offspring probability generating function.

On the existence of submultiplicative moments for the stationary distributions of some Markovian random walks

1999 ◽  
Vol 36 (01) ◽  
pp. 78-85
Author(s):  
M. S. Sgibnev
Keyword(s):  
Markov Chains ◽  
Random Walks ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Necessary And Sufficient Conditions ◽  
Stationary Distributions ◽  
Necessary And Sufficient ◽  
Submultiplicative Function ◽  
Independent Identically Distributed

This paper is concerned with submultiplicative moments for the stationary distributions π of some Markov chains taking values in ℝ+ or ℝ which are closely related to the random walks generated by sequences of independent identically distributed random variables. Necessary and sufficient conditions are given for ∫φ(x)π(dx) &lt; ∞, where φ(x) is a submultiplicative function, i.e. φ(0) = 1 and φ(x+y) ≤ φ(x)φ(y) for all x, y.

Quasi-stationary distributions for Markov chains on a general state space

1974 ◽  
Vol 11 (04) ◽  
pp. 726-741 ◽  
Author(s):  
Richard. L. Tweedie
Keyword(s):  
Markov Chain ◽  
Invariant Measure ◽  
Markov Chains ◽  
State Space ◽  
Finiteness Condition ◽  
General State ◽  
Stationary Distributions ◽  
General State Space ◽  
Countably Infinite ◽  
Stationary Behaviour

The quasi-stationary behaviour of a Markov chain which is φ-irreducible when restricted to a subspace of a general state space is investigated. It is shown that previous work on the case where the subspace is finite or countably infinite can be extended to general chains, and the existence of certain quasi-stationary limits as honest distributions is equivalent to the restricted chain being R-positive with the unique R-invariant measure satisfying a certain finiteness condition.

scholarly journals On the construction problem for single-exit Markov chains

1991 ◽  
Vol 43 (3) ◽  
pp. 439-450 ◽  
Author(s):  
P.K. Pollett
Keyword(s):  
Invariant Measure ◽  
Markov Chains ◽  
State Space ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Construction Problem ◽  
Necessary And Sufficient

I shall consider the following problem: given a stable, conservative, single-exit q-matrix, Q, over an irreducible state-space S and a μ-subinvariant measure, m, for Q, determine all Q-processes for which m is a μ-invariant measure. I shall provide necessary and sufficient conditions for the existence and uniqueness of such a process.

Institutional Specifics of Business Self-regulation

2003 ◽  
pp. 88-98 ◽  
Author(s):  
A. Obydenov
Keyword(s):  
Economic Activity ◽  
Self Regulation ◽  
Institutional Arrangement ◽  
Voluntary Membership ◽  
Sufficient Set ◽  
The Subject ◽  
Necessary And Sufficient ◽  
Object Of Control ◽  
Self Enforcement

Self-regulation appears to be a special institution where economic actors establish their own rules of economic activity for themselves in a specific business field. At the same time they are the object of control within these rules and the subject of legal management of the controller. Self-regulation contains necessary prerequisites for fundamental resolution of the problem of "controlling the controller". The necessary and sufficient set of five self-regulation organization functions provides efficiency of self-regulation as the institutional arrangement. The voluntary membership in a self-regulation organization is essential for ensuring self-enforcement of institutional arrangement of self-regulation.

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