论文信息 - On Harris Recurrence in Continuous Time

On Harris Recurrence in Continuous Time

We show that a continuous-time Markov process X is Harris recurrent if and only if there exists a nonzero α-finite measure I½ on its state space such that X surely hits sets with positive I½-measure. This simple criterion is applied to some nonparametric closed queueing networks.

Avishai Mandelbaum | Haya Kaspi | A. Mandelbaum | H. Kaspi

[1] Robert L. Smith,et al. Hit-and-Run Algorithms for Generating Multivariate Distributions , 1993, Math. Oper. Res..

[2] Karl Sigman,et al. Queues as Harris recurrent Markov chains , 1988, Queueing Syst. Theory Appl..

[3] Sلأren Asmussen,et al. Applied Probability and Queues , 1989 .

[4] S. Meyn,et al. Stability of Markovian processes II: continuous-time processes and sampled chains , 1993, Advances in Applied Probability.

[5] A. W. Kemp,et al. Applied Probability and Queues , 1989 .

[6] T. E. Harris. The Existence of Stationary Measures for Certain Markov Processes , 1956 .

[7] S. Asmussen. On Coupling and Weak Convergence to Stationarity , 1992 .

[8] J. Azema,et al. Propriétés relatives des processus de Markov récurrents , 1969 .

[9] H. Kaspi. On invariant measures and dual excursions of Markov processes , 1984 .

[10] K. Sigman. NOTES ON THE STABILITY OF CLOSED QUEUEING NETWORKS , 1989 .

[11] Sean P. Meyn,et al. Stability of Generalized Jackson Networks , 1994 .

[12] E. Nummelin,et al. A splitting technique for Harris recurrent Markov chains , 1978 .

[13] A. Mandelbaum,et al. Regenerative closed queueing networks , 1992 .

[14] A. Borovkov. Limit Theorems for Queueing Networks. I , 1987 .

[15] L. Rogers. GENERAL THEORY OF MARKOV PROCESSES , 1989 .

[16] K. Athreya,et al. A New Approach to the Limit Theory of Recurrent Markov Chains , 1978 .