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Drift vectors are not sufficient to determine recurrence of a Markov chain on ℤ3 +

  • Mitchell Kotler (a1)
Abstract

For a Markov chain in n = 2, drift vectors (conditional expected jumps) on the interior and the boundaries distinguish between recurrence and transience. The result of this paper is that the analogous proposition in the n = 3 case fails.

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Postal address: Department of Mathematics and Statistics, UMass Amherst, Amherst, MA 01003, USA.
References
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Fayolle, G. (1989) On random walks arising in queueing systems: ergodicity and transience via quadratic forms as Lyapounov functions – Part I. Queueing Systems 5, 167184.
Foster, F. G. (1953) On the stochastic matrices associated with certain queueing processes. Ann. Math. Statist. 24, 355360.
Malyshev, V. A. (1972) Classification of two-dimensional positive random walks and almost linear semi-martingales. Sov. Math. Dokl. 13, 136139.
Rosenkrantz, W. (1989) Ergodicity conditions for two-dimensional Markov chains on the positive quadrant. Prob. Theory Rel. Fields 83, 309319.
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Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
  • URL: /core/journals/journal-of-applied-probability
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