Sufficient conditions for regularity, recurrence and ergodicity of Markov processes
- 1 July 1975
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 78 (1) , 125-136
- https://doi.org/10.1017/s0305004100051562
Abstract
Two sets of conditions are found on the Q-matrix of an irreducible Markov process on a countably infinite state space which ensure that Q is regular; the first set also implies that the Markov process is ergodic, the second that it is recurrent. If the process is not irreducible, the conditions still imply regularity, and then either non-dissipativity or ‘ultimate recurrence’ (reducible analogues of ergodicity and recurrence) of the process. Conditions sufficient for ergodicity or recurrence of the process in the non-regular and regular case are also given. The results parallel (and use) results for discrete time Markov chains, and the known discrete time recurrence condition is extended to the reducible case. The conditions are illustrated by a competition process example.Keywords
This publication has 10 references indexed in Scilit:
- SOME ERGODIC PROPERTIES OF THE FELLER MINIMAL PROCESSThe Quarterly Journal of Mathematics, 1974
- The calculation of limit probabilities for denumerable Markov processes from infinitesimal propertiesJournal of Applied Probability, 1973
- Some Conditions for Ergodicity and Recurrence of Markov ChainsOperations Research, 1969
- Stationarity Equations in Continuous Time Markov ChainsTransactions of the American Mathematical Society, 1963
- On non-dissipative Markov chainsMathematical Proceedings of the Cambridge Philosophical Society, 1957
- Denumerable Markov processes and the associated contraction semigroups on lActa Mathematica, 1957
- On the Stochastic Matrices Associated with Certain Queuing ProcessesThe Annals of Mathematical Statistics, 1953
- On Markov chains with an enumerable infinity of statesMathematical Proceedings of the Cambridge Philosophical Society, 1952
- On non-dissipative Markoff chains with an enumerable infinity of statesMathematical Proceedings of the Cambridge Philosophical Society, 1951
- Markoff chains with an enumerable number of states and a class of cascade processesMathematical Proceedings of the Cambridge Philosophical Society, 1951