Craven, B. D. Perturbed Markov processes. (English) Zbl 1022.60066 Stoch. Models 19, No. 2, 269-285 (2003). Summary: A Markov process in discrete time is perturbed by a small parameter. A perturbation theory is constructed, both for a time-dependent process, and for a stationary state. Some queueing applications are discussed. Cited in 1 Document MSC: 60J05 Discrete-time Markov processes on general state spaces Keywords:perturbation theory; queueing applications PDFBibTeX XMLCite \textit{B. D. Craven}, Stoch. Models 19, No. 2, 269--285 (2003; Zbl 1022.60066) Full Text: DOI References: [1] Seneta E., Numerical Solution of Markov Chains pp 121– (1991) [2] Van Dijk N.M., Adv. Appl. Probab. 20 pp 99– (1988) · Zbl 0642.60099 · doi:10.2307/1427272 [3] Sil’vestrov D.S., Theor. Probab. Math. Stat. 45 pp 105– (1992) [4] Sil’vestrov D.S., Theor. Probab. Math. Stat. 48 pp 125– (1994) [5] Korolyuk V.S., Mathematical Foundations of the State Lumping of Large Systems (1993) · doi:10.1007/978-94-011-2072-2 [6] Kartashov N.V., Strong Stable Markov Chains (1996) [7] Meyer C.D., SIAM Rev. 17 pp 443– (1975) · Zbl 0313.60044 · doi:10.1137/1017044 [8] Schweitzer P.J., J. Appl. Probab. 5 pp 401– (1968) · Zbl 0196.19803 · doi:10.2307/3212261 [9] Avrachenkov K.E., Handbook of Markov Decision Processes (2002) [10] Cohen J.W., J. Appl. Probab. 4 pp 343– (1967) · Zbl 0153.20101 · doi:10.2307/3212028 [11] Kingman J.F.C., J. Appl. Probab. 3 pp 385– (1966) [12] Kato T., Perturbation Theory for Linear Operators (1966) · Zbl 0148.12601 [13] Craven B.D., J. Aust. Math. Soc. 5 pp 299– (1965) · Zbl 0147.16502 · doi:10.1017/S1446788700027737 [14] Craven B.D., J. Appl. Probab. 6 pp 573– (1969) · Zbl 0191.50402 · doi:10.2307/3212103 [15] Goldberg S., Unbounded Linear Operators (1966) · Zbl 0148.12501 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.