A note on the infinitely deep dam with a Markovian input

1979 ◽  
Vol 16 (4) ◽  
pp. 917-922 ◽  
Author(s):  
R. M. Phatarfod
Keyword(s):  
Markov Chain ◽  
General Solution ◽  
Unit Disc ◽  
Linear Constraints ◽  
Equilibrium Equations ◽  
Ergodic Markov Chain

In this paper we consider an infinitely deep dam fed by inputs which form an ergodic Markov chain and whose release M is non-unit. The extension to non-unit release follows on lines similar to the independent inputs case. We show that P(θ) – θ MΙ where P(θ) = (pijθ i) has a maximum of N = M(M + l)/2 non-zero singularities in the unit disc, so that the general solution of the equilibrium equations has N unknown constants. We also show that these constants satisfy N linear constraints, so that the solution is fully determined.

A note on the infinitely deep dam with a Markovian input

1979 ◽  
Vol 16 (04) ◽  
pp. 917-922
Author(s):  
R. M. Phatarfod
Keyword(s):  
Markov Chain ◽  
General Solution ◽  
Unit Disc ◽  
Linear Constraints ◽  
Equilibrium Equations ◽  
Ergodic Markov Chain

In this paper we consider an infinitely deep dam fed by inputs which form an ergodic Markov chain and whose release M is non-unit. The extension to non-unit release follows on lines similar to the independent inputs case. We show that P(θ) – θ MΙ where P(θ) = (pijθ i ) has a maximum of N = M(M + l)/2 non-zero singularities in the unit disc, so that the general solution of the equilibrium equations has N unknown constants. We also show that these constants satisfy N linear constraints, so that the solution is fully determined.

An extension of a theorem concerning an interesting Markov chain

1973 ◽  
Vol 10 (4) ◽  
pp. 886-890 ◽  
Author(s):  
W. J. Hendricks
Keyword(s):  
Markov Chain ◽  
Stationary Distribution ◽  
Ergodic Markov Chain ◽  
The Right

In a single-shelf library of N books we suppose that books are selected one at a time and returned to the kth position on the shelf before another selection is made. Books are moved to the right or left as necessary to vacate position k. The probability of selecting each book is assumed to be known, and the N! arrangements of the books are considered as states of an ergodic Markov chain for which we find the stationary distribution.

scholarly journals Markov chains with exponential return times are finitary

2020 ◽  
pp. 1-9
Author(s):  
OMER ANGEL ◽  
YINON SPINKA
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Renewal Process ◽  
Proper Subgroup ◽  
Ergodic Markov Chain ◽  
Countable State Space ◽  
Return Times ◽  
Exponential Tails ◽  
Stationary Version ◽  
Countable State

Abstract Consider an ergodic Markov chain on a countable state space for which the return times have exponential tails. We show that the stationary version of any such chain is a finitary factor of an independent and identically distributed (i.i.d.) process. A key step is to show that any stationary renewal process whose jump distribution has exponential tails and is not supported on a proper subgroup of ℤ is a finitary factor of an i.i.d. process.

Regeneration in tandem queues with multiserver stations

1988 ◽  
Vol 25 (02) ◽  
pp. 391-403 ◽  
Author(s):  
Karl Sigman
Keyword(s):  
Markov Chain ◽  
Renewal Process ◽  
Single Server ◽  
Tandem Queues ◽  
Random Assignment ◽  
Tandem Queue ◽  
Ergodic Markov Chain ◽  
Fifo Queue ◽  
Harris Chain ◽  
Server System

A tandem queue with a FIFO multiserver system at each stage, i.i.d. service times and a renewal process of external arrivals is shown to be regenerative by modeling it as a Harris-ergodic Markov chain. In addition, some explicit regeneration points are found. This generalizes the results of Nummelin (1981) in which a single server system is at each stage and the result of Charlot et al. (1978) in which the FIFO GI/GI/c queue is modeled as a Harris chain. In preparing for our result, we study the random assignment queue and use it to give a new proof of Harris ergodicity of the FIFO queue.

Fast matching via ergodic markov chain for super-large graphs

2020 ◽  
Vol 106 ◽  
pp. 107418
Author(s):  
Yali Zheng ◽  
Lili Pan ◽  
Jiye Qian ◽  
Hongliang Guo
Keyword(s):  
Markov Chain ◽  
Large Graphs ◽  
Ergodic Markov Chain

Optimal rate for support vector machine regression with Markov chain samples

2014 ◽  
Vol 12 (06) ◽  
pp. 1450045 ◽  
Author(s):  
Jie Xu
Keyword(s):  
Support Vector Machine ◽  
Markov Chain ◽  
Hilbert Spaces ◽  
Reproducing Kernel ◽  
Support Vector ◽  
Support Vector Machine Regression ◽  
Optimal Learning ◽  
Ergodic Markov Chain ◽  
Generalization Ability ◽  
Kernel Hilbert Spaces

Support vector machine regression (SVMR) is a regularized learning method in reproducing kernel Hilbert spaces with epsilon-insensitive loss function. Different from the previously known works on the generalization ability of SVMR with independent and identically distributed (i.i.d.) samples, in this paper, we consider the generalization ability of SVMR algorithm based on non-i.i.d. samples, uniformly ergodic Markov chain (u.e.M.c.) samples. We give an error analysis for SVMR algorithm based on u.e.M.c. samples and obtain the optimal learning rate for the SVMR algorithm based on u.e.M.c. samples.

scholarly journals Discrepancy bounds for uniformly ergodic Markov chain quasi-Monte Carlo

2016 ◽  
Vol 26 (5) ◽  
pp. 3178-3205 ◽  
Author(s):  
Josef Dick ◽  
Daniel Rudolf ◽  
Houying Zhu
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Ergodic Markov Chain ◽  
Quasi Monte Carlo
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