A note on the two-sided regulated random walk. (Q1426657)
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scientific article; zbMATH DE number 2057145
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A note on the two-sided regulated random walk. |
scientific article; zbMATH DE number 2057145 |
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A note on the two-sided regulated random walk. (English)
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15 March 2004
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Random walks on the integers regulated by confinement to the interval \([0, N]\) are investigated with respect to their limiting behaviour as the upper bound \(N\) tends to infinity. It is shown that under quite natural assumptions after rescaling to the interval \([0, 1]\) the limiting stationary distribution is uniform, the rate of convergence in all \(p\)-norms being \(1/N\). By use of generating functions the authors state and prove two theorems and several lemmata that deserve interest in themselves. They illustrate their results by three examples, two of them from queueing theory.
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Markov chain
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regulated random walk
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stochastic ordering
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convergence rate
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0.7673546075820923
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0.7436652183532715
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