Random record processes and state dependent thinning
作者： Sid Browne , John Bunge
DOI: 10.1016/0304-4149(94)00022-L
关键词: Markov process 、 Stochastic process 、 Discrete mathematics 、 Compound Poisson process 、 Fractional Poisson process 、 Renewal theory 、 Cox process 、 Poisson distribution 、 Point process 、 Mathematics 、 Calculus
摘要: Abstract Suppose that a point process N t = T 1 , 2 … if [0, ∞) is thinned by independently retaining Tn with probability pn. Our main examples are the classical p-thinning (pn ≡ p) and random record ( p n ). When mixed, nonhomogeneous Poisson process, we find conditions under which Poisson. pure birth (gamma-mixed exponential rate), show Markov renewal, an interesting structure, compare this related asymptotic results. Mittag-Leffler renewal (the homogeneous special case), give “Deheuvels-type” representation of (Deheuvels, 1982) characterization
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sci-hub.se 参考文章(17)
William J. Anderson, Continuous-Time Markov Chains Springer Series in Statistics. ,(1991) , 10.1007/978-1-4612-3038-0
Pierre Brémaud, Point Processes and Queues Springer New York. ,(1981) , 10.1007/978-1-4684-9477-8
J.A. Bunge, H.N. Nagaraja, The distributions of certain record statistics from a random number of observations Stochastic Processes and their Applications. ,vol. 38, pp. 167- 183 ,(1991) , 10.1016/0304-4149(91)90077-P
Sidney I. Resnick, Extreme Values, Regular Variation, and Point Processes ,(1987)
F.T. Bruss, L.C.G. Rogers, Pascal processes and their characterization Stochastic Processes and their Applications. ,vol. 37, pp. 331- 338 ,(1991) , 10.1016/0304-4149(91)90052-E
Elja Arjas, Pentti Haara, Ikka Norros, Filtering the histories of a partially observed marked point process Stochastic Processes and their Applications. ,vol. 40, pp. 225- 250 ,(1992) , 10.1016/0304-4149(92)90013-G
F. Thomas Bruss, Stephen M. Samuels, Conditions for Quasi-Stationarity of the Bayes Rule in Selection Problems with an Unknown Number of Rankable Options Annals of Probability. ,vol. 18, pp. 877- 886 ,(1990) , 10.1214/AOP/1176990864
Fred Böker, Richard Serfozo, Ordered thinnings of point processes and random measures Stochastic Processes and their Applications. ,vol. 15, pp. 113- 132 ,(1983) , 10.1016/0304-4149(83)90051-0
R. N. Pillai, On Mittag-Leffler functions and related distributions Annals of the Institute of Statistical Mathematics. ,vol. 42, pp. 157- 161 ,(1990) , 10.1007/BF00050786
F.W. Steutel, Some recent results in infinite divisibility Stochastic Processes and their Applications. ,vol. 1, pp. 125- 143 ,(1973) , 10.1016/0304-4149(73)90008-2