Skip to main content

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

  • Mitchell Kotler (a1)

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.

Corresponding author
Postal address: Department of Mathematics and Statistics, UMass Amherst, Amherst, MA 01003, USA.
Hide All
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.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
  • URL: /core/journals/journal-of-applied-probability
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


MSC classification


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed