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A Bibliography on Semi-Markov Processes BIBLIOGRAPHY 004 CORE Metadata, citation and similar papers at core.ac.uk Provided by Elsevier - Publisher Connector A bibliography on semi-Markov processes BIBLIOGRAPHY 004 Jozef L. Teugels (*) INTRODUCTION At the appearance of this bibliography we want to thank warmly all those who have helped compiling this edition by sending us titles of publications, preprints, reprints and other re- levant information. Especially Cheong C. Kong and Jos H.A. de Smit have contributed at an early stage. All publications by the same author have been arranged by the year of publication. This will be convenient if in the future we should decide to publish a supplement to this bibliography. The present version contains about 600 papers written by some 300 authors. We have indicated to the best of our kwowledge where a publication has been reviewed or summarized. We write ST for Statistical Theory and Method Abstracts, MR for Mathematical Reviews and Zbl for Zentralblatt fiir Mathematik und ihre Grenzgebiete. The first number refers to the volume and the second to the number of the page (for Zbl) or review/abstract (for ST and MR). Thus MR 27-1999 refers to review number" 1999 of volume 27 of Mathe- matical Reviews.. We follow MR in our abbreviations and transliterations for the names of journals. The reader's attention is drawn on translations made of journals published in Russian. The index volumes of MR should be consulted. New information can always be forwarded to the author. BIBLIOGRAPHY Akimov A.P. and Pogosjan I.A. Andronov A.M. and Gertsbakh I.G. On structural reservation systems with repair and cold reser- On properties of multidimensional functionals on semi-Mar- vation 1974 kov processes with finite state space. 1972a (Kussian). Kibernetika, 1974, 91-95. Zbl : 275-509. (Russian). Kybernetika, 1972, 118-122. MR : 47-1150, Zbl : 293-416. Aladzev B.M. Application of semi-Markov processes in estimating the re- Andronov A.M. and Rosenblit P. Ya. liability of separable duplicating systems. 1972a Statistics of semi-Markov birth and death processes and their {Russian). Avtomat. vy~islit. Tehn. Riga. Zbl : 245-400. application to the analysis of complex queueing systems. 1972a Aleksandrov Ju. A. and Jancevi~ A.A. (Kussian). Izvestija Akad. Nauk. SSSK, Tehn. Kibernet., 3, Some classes of stochastic processes with after effect.1970a 1972, 113-120. Zbl : 283-349. (Russian). Vestnik Har'kov. Gos. Univ., 53 , 139-157. MR : 44-1091. AniSimov V.V. Limit theorems for semi-Markov processes with a countable Anderson L.B. set of states. 1970a Filtered semi-Markov processes. 1967a Soviet Math. Dokl., 11,945-948. MR : 42-3851, Zbl : 228- M. So. Thesis. Northwestern University. 340. Limit distributions of functionals of a semi-Markov process Markov renewal theory on the whole line. 1971a given on a fixed set of states, up to the time of first exit. Ph.D. Thesis, Northwestern University, Evanston (Ill.), 1970b U.S.A. Soviet Math. Dokl., 11, 1002-1005, MR : 42-3852, Zbl : 228-340. (*) J.L. Teugels, Katholieke Universiteit te Leuven, Celestijnenlaan 200 B, 3030 Heverlee, Belgium. Journal of Computational and Applied Mathematics, volume 2, no 2, 1976. 125 Anisimov V.V. Some theorems on limit distributions for sums of random On the asymptotic behaviour of a generalization of Markov variables connected into the homogeneous Markov Chain. renewal processes. 1972b 1970c Soc. Sci. Fenn. Comment. Phys.-Math., 42, i7-25. MR : 47- Dopovidi Akad. Nauk. Ukrain. RSR, Ser. A, 99-103. 1146, Zbl : 238-424. (English summary). MR : 44.3390, Zbl : 194-496. On the use of a fundamental identity in the theory of semi- Limit theorems for semi-Markov processes, I. 1970d Markov queues. 1972c (Russian). Teor. Verojatnost. i Mat. Statist., 2, 3-12. MR : Advances Appl. Probability, 4, 271-284. ST : 14-1651, MR : 43-5624, Zbl : 222-403. 49-4115, Zbl : 243-417. Limit theorems for semi-Markov processes, II. 1970e Arjas Elja and Speed Terrance P. (Russian). Teor. Verojatnost. i Mat. Statist., 2, 13-21. MR : An extension of Cramer's estimate for the absorption proba- 43-5624, Zbl : 222-403. bility of a random walk. 1973a Multidimensional limit theorems for semi-Markov processes proc. Camb. Philos. Soc. ST : 14-1652. with a countable set of states. 1970f Symmetric Wiener-Hopf factorizations in Markov additive pro- (Russian). Teor. Verojatnost. i Mat. Statist., 3, 3-15. MR : cesses. 1973b 45-2809, Zbl : 238-424. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 26, 105-118. Limit theorems for sums of random variables on Markov MR : 48-9848, Zbl : 244-413. chains, connected with the exit from a set, forming a class Topics in Markov additive processes. 1973c in the limit. 1971a Math. Scandinav., 32L, 171-192. MR : 49-6369, Zbl : 277-369. (Russian). Teor. Verojatnost. i Mat. Statist., 4, 3-17. MR : 44.7648, Zbl : 225-383. A stopping problem in Markov additive processes. 1973d Advances Appl. Probability, 5, 2-3. Limit theorems for sums of random variables, in series sche- me, given on a subset of states of a Markov chain up to the Arseni~vili G.L. instant of exit. 1971b Some queries on semi-Markov processes of order r. 1970a (Russian). Teor. Verojamost. i Mat. Statist., 4, 18-26. MR : (Russian). Voprosy razrab, i vnedrenija, sredstv vy~isl, tehn. 44-7649, Zbl : 225-383. Thilisi, 128-132. On the summation of random variables on a Markov chain On a class of functionals for complex semi-Markov processes with a countable splitting set of states. 1972a with discrete intervention of chance. 1970b Doklady Akad. Nauk. SSSR, 203 , 735-737. Soviet Math. (Russian). Sakharth. SSR Mecn. Akad. Moambe, 58, 25-28 Dokl., 13,431-434, Zbl : 264-380. (English summary). MR : 43-4136, Zbl : 195-477. The limiting behaviour of a semi-Markovian process with a On a problem in the theory of mass service. 1971a decomposable state space. 1972b (Russian). Sakharth. SSR Mecn. Akad. Moambe, 59, 545-548 Doklady Akad. Nauk. SSSR., 206, 777-779. Soviet Math. (English summary). Zbl : 205-485. Dokl., 13, 1276-1279. MR : 47-2685, Zbl : 266-361. Certain limit theorems for semi-Markov processes with coun- Arseni~vili G.L. and E~ov LI. table state space in a scheme of series. 1972c The distribution of the sojourntime in a given region of a semi- (Russian). Teor. Verojatnost. i Mat. Statist., 6, 3-13. MR : Markov process of order r. 1969a 46-8296, Zbl : 284-383. RUSsian). Thbilis. Sahelmc. Univ. Gamogeneb. Math. I~sti. om., 2, 151-157. MR : 43-4135. Limit theorems for random processes with a splitting set of states. 1972d A certain limit tlaeorem for semi-Markov processes or order r. (Russian). Doldady Akad. Nauk. SSSR, 210, 1001-1003. 1969b MR : 50-3305. (Russian; Georgian and English summaries). Sakharth. SSR Mecn. Akad. Moambe, .53_, 25-28. ME : 40-6624, Zbl : 196- Asymptotic consolidation of the states of stochastic pro- 199. cesses. 1973a (Russian). Kibernetika, 1973, 109-118. MR : 49-6350, Zbl : A generalization of Markov chains with semi-Markov interven- 273-364. tion of chance. 1969c (Russian; Georgian and English summaries). Sakharth. SSR Limit theorems for sums of random variables defined on a Mecn. Akad. Moambe. 54, 285-288. MR : 41-1113, Zbl : countable subset of a Markov chain up to time of exit. 177-218. 1973b (Russian). Teor. Verojatnost. i Mat. Statist., 8, 3-13. Zbl : Arseni~vili G.L. and Prizva G.I. 274-375. On the distribution of the size of the first jump of a semi- Markov process of order r over a random level. 1972a Annaev T. (Russian. English summary I. Soohscenija Akad. Nauk, Gruzin. A certain problem in queueing theory with semi-Markov SSR. 68, 297-300, Zbl : 244.416, MR : 50-5968. servicing of demands. 1971a (Russian), Izv. Akad. Nauk. Turkmen. SSR. Ser. Fiz.-Tehn. Arseven Ersen and Kshirsagar Anant M. Him. Geol. Nauk., 3, 98-100. MR : 47-1152. Stationary state probabilities of a Markov renewal process and optimum scores associated with the states. 1974a Anselone Philip M. Commun. Statist., 3, 923-931. Zbl : 295-371. Ergodic theory for discrete semi-Markov chains. 1960a Duke Math. J., 27, 33-40. MR : 22-12567. Zbl : 104.370. Asakura T. and Osaki Shunji. Limit theorems for semi-Markov processes. Part L 1960b A two-unit standby redundant system with repair and preven- Amer. Math. Monthly, 67, 565-566. tive maintenance. 1970a J. Appl. Probability, 7, 541-648. Arias Elja On a fundamental identity in the theory of semi-Markov Bandura V.N. and E~ov I.L processes. 1972a The distribution of the first passage time of a given level for Advances Appl. probability, 4, 258~270, ST : 14.1650, a certain class of functions with steplike trajectories, I, IL MR : 49-4114, Zbl : 243-417. 1970a (Russian-English summary). Teor. Verojamost. i Mat. Statist., 1, 7-21 and 22-36. MR : 43-1258, Zbl : 259-395. Journal of Computational and Applied Mathematics, volume 2, no 2, 1976. 126 Barlow Richard E. Borovkov A.A. A~lications of semi-Markov processes to counter and re- Certain problems for controlled stochastic processes. 1964a liability problems. 1962a Sibvisk. Mat. ~, 5., 996-1006. Ph. D. Thesis. Techn. Rep. 57, Appl. and Stat. Labs., Stan- ford University, Stanford. On convergence of weakly dependent processes to the Wiener process. 1968a Applications of semi-Markov processes to counter problems. Theor. Probability Appl., 12, 159-186. Zbl : 214-162. 1962b Studies in Appl. Probabs~ity and Management Sc. ed. Arrow, Borovkov A.A. and Rogosin B.A. garlin, Scarf. Stanford University Press, Stanford, Cal., 34-62. Boundary problems for certain two-dimensional random MR : 25.2641,Zbl : 116-105. variables. 1964a Theor.
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