Poisson theorem for non-homogeneous Markov chains

1989 ◽  
Vol 26 (03) ◽  
pp. 637-642 ◽  
Author(s):  
Janusz Pawłowski
Keyword(s):  
Markov Chains ◽  
Poisson Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Compound Poisson Distribution ◽  
Convergence In Distribution ◽  
Compound Poisson ◽  
Necessary And Sufficient

This paper gives necessary and sufficient conditions for the convergence in distribution of sums of the 0–1 Markov chains to a compound Poisson distribution.

Poisson theorem for non-homogeneous Markov chains

1989 ◽  
Vol 26 (3) ◽  
pp. 637-642 ◽  
Author(s):  
Janusz Pawłowski
Keyword(s):  
Markov Chains ◽  
Poisson Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Compound Poisson Distribution ◽  
Convergence In Distribution ◽  
Compound Poisson ◽  
Necessary And Sufficient

This paper gives necessary and sufficient conditions for the convergence in distribution of sums of the 0–1 Markov chains to a compound Poisson distribution.

scholarly journals Poisson distribution series on a general class of analytic functions

2020 ◽  
Vol 24 (2) ◽  
pp. 241-251
Author(s):  
Basem A. Frasin
Keyword(s):  
Integral Operator ◽  
Poisson Distribution ◽  
Analytic Functions ◽  
General Class ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Class A ◽  
Poisson Distribution Series ◽  
Necessary And Sufficient

The main object of this paper is to find necessary and sufficient conditions for the Poisson distribution series to be in a general class of analytic functions with negative coefficients. Further, we consider an integral operator related to the Poisson distribution series to be in this class. A number of known or new results are shown to follow upon specializing the parameters involved in our main results.

scholarly journals Necessary and sufficient conditions for recurrence and transience of Markov chains, in terms of inequalities

1978 ◽  
Vol 15 (4) ◽  
pp. 848-851 ◽  
Author(s):  
Jean-François Mertens ◽  
Ester Samuel-Cahn ◽  
Shmuel Zamir
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
State Space ◽  
Bounded Solution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Existence Of A Solution ◽  
Necessary And Sufficient ◽  
Irreducible Markov Chain

For an aperiodic, irreducible Markov chain with the non-negative integers as state space it is shown that the existence of a solution to in which yi → ∞is necessary and sufficient for recurrence, and the existence of a bounded solution to the same inequalities, with yk < yo, · · ·, yN–1 for some k ≧ N, is necessary and sufficient for transience.

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.

scholarly journals An Application of a Poisson Distribution Series on Certain Analytic Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-3 ◽  
Author(s):  
Saurabh Porwal
Keyword(s):  
Integral Operator ◽  
Poisson Distribution ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Poisson Distribution Series ◽  
Necessary And Sufficient

The purpose of the present paper is to introduce a Poisson distribution series and obtain necessary and sufficient conditions for this series belonging to the classes T(λ,α) and C(λ,α). We also consider an integral operator related to this series.

Hendricks libraries and Tsetlin piles

1982 ◽  
Vol 14 (01) ◽  
pp. 37-55 ◽  
Author(s):  
Jacques-Edouard Dies
Keyword(s):  
Markov Chains ◽  
Large Class ◽  
Special Class ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Stationary Measure ◽  
Sufficient Condition ◽  
Positive Recurrence ◽  
Necessary And Sufficient

In order to study the transience of Hendricks libraries, we introduce and study a special class of Markov chains, the Tsetlin d-piles, generalizing Tsetlin libraries and briefly defined as follows: a 1-pile is a Tsetlin library and a d-pile is a Tsetlin library where each book is replaced by a (d − 1)-pile. We give a stationary measure of these chains and establish the necessary and sufficient conditions for positive recurrence and transience. Finally, the study of d-piles allows us to determine a sufficient condition for transience of quite a large class of Hendricks libraries.

Limiting second moments for transient states of Markov chains

1973 ◽  
Vol 10 (04) ◽  
pp. 891-894
Author(s):  
H. P. Wynn
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Covariance Matrix ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Time Points ◽  
Transient States ◽  
Second Moments ◽  
Necessary And Sufficient

The set of transient states of a Markov chain is considered as a system. If numbers of arrivals to the system at discrete time points have constant mean and covariance matrix then there is a limiting distribution of numbers in the states. Necessary and sufficient conditions are given for this distribution to yield zero correlations between states.

scholarly journals Invariant probabilities for Feller-Markov chains

1995 ◽  
Vol 8 (4) ◽  
pp. 341-345 ◽  
Author(s):  
Onésimo Hernández-Lerma ◽  
Jean B. Lasserre
Keyword(s):  
Markov Chains ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Probability Measures ◽  
Feller Property ◽  
Necessary And Sufficient

We give necessary and sufficient conditions for the existence of invariant probability measures for Markov chains that satisfy the Feller property.

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.

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