On the distribution of the supremum for stochastic processes with interchangeable increments
HTML articles powered by AMS MathViewer
- by Lajos Takács PDF
- Trans. Amer. Math. Soc. 119 (1965), 367-379 Request permission
References
-
D. André, Solution directe du problème résolu par M. Bertrand, C. R. Acad. Sci. Paris 105 (1887), 436-437.
É. Barbier, Généralisation du problème résolu par M.J. Bertrand, C. R. Acad. Sci. Paris 105 (1887), 407.
- Glen Baxter and M. D. Donsker, On the distribution of the supremum functional for processes with stationary independent increments, Trans. Amer. Math. Soc. 85 (1957), 73–87. MR 84900, DOI 10.1090/S0002-9947-1957-0084900-X
- Václav E. Beneš, General stochastic processes in the theory of queues, Addison-Wesley Publishing Co., Inc., Reading, Mass.-Palo Alto, Calif.-London, 1963. MR 0152034 J. Bertrand, Solution d’un problème, C. R. Acad. Sci. Paris 105 (1887), 369.
- K. L. Chung and W. H. J. Fuchs, On the distribution of values of sums of random variables, Mem. Amer. Math. Soc. 6 (1951), 12. MR 40610
- D. A. Darling, The maximum of sums of stable random variables, Trans. Amer. Math. Soc. 83 (1956), 164–169. MR 80393, DOI 10.1090/S0002-9947-1956-0080393-6
- J. Gani and N. U. Prabhu, A storage model with continuous infinitely divisible inputs, Proc. Cambridge Philos. Soc. 59 (1963), 417–429. MR 146906, DOI 10.1017/s030500410003704x
- J. Gani and R. Pyke, The content of a dam as the supremum of an infinitely divisible process, J. Math. Mech. 9 (1960), 639–651. MR 0121877, DOI 10.1512/iumj.1960.9.59038
- J. L. W. V. Jensen, Sur une identité d’Abel et sur d’autres formules analogues, Acta Math. 26 (1902), no. 1, 307–318 (French). MR 1554966, DOI 10.1007/BF02415499
- David G. Kendall, Some problems in theory of dams, J. Roy. Statist. Soc. Ser. B 19 (1957), 207–212; discussion 212–233. MR 92290, DOI 10.1111/j.2517-6161.1957.tb00257.x A. Kolmogorov, Sur la loi forte des grandes nombres, C.R. Acad. Sci. Paris 191 (1930), 910-911.
- P. A. P. Moran, A probability theory of a dam with a continuous release, Quart. J. Math. Oxford Ser. (2) 7 (1956), 130–137. MR 101573, DOI 10.1093/qmath/7.1.130
- Harry Pollard, The representation of $e^{-x^{\lambda }}$ as a Laplace integral, Bull. Amer. Math. Soc. 52 (1946), 908–910. MR 18286, DOI 10.1090/S0002-9904-1946-08672-3
- Ronald Pyke, The supremum and infimum of the Poisson process, Ann. Math. Statist. 30 (1959), 568–576. MR 107315, DOI 10.1214/aoms/1177706269
- N. V. Smirnov, Approximate laws of distribution of random variables from empirical data, Uspehi Matem. Nauk 10 (1944), 179–206 (Russian). MR 0012387
- Lajos Takács, Investigation of waiting time problems by reduction to Markov processes, Acta Math. Acad. Sci. Hungar. 6 (1955), 101–129 (English, with Russian summary). MR 70888, DOI 10.1007/BF02021270
- Lajos Takács, The probability law of the busy period for two types of queuing processes, Operations Res. 9 (1961), 402–407. MR 125658, DOI 10.1287/opre.9.3.402
- Lajos Takács, Introduction to the theory of queues, University Texts in the Mathematical Sciences, Oxford University Press, New York, 1962. MR 0133880
- Lajos Takács, Combinatorial methods in the theory of dams, J. Appl. Probability 1 (1964), 69–76. MR 162296, DOI 10.1017/s0021900200111556
Additional Information
- © Copyright 1965 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 119 (1965), 367-379
- MSC: Primary 60.60
- DOI: https://doi.org/10.1090/S0002-9947-1965-0208671-3
- MathSciNet review: 0208671