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Abstract: s (which includes the geometric tails of some of our queueing examples) is given by Goldie [26]. C34 Rice's formula. Formalizations of the "local" version of the heurstic from Rice's formula P (M t ? b) ¸ tae b as b ! 1; t fixed are given by Albin [2] C41 Stein's method for extremes of stationary sequences. Barbour et al [13] study the Poisson approximation for the sojourn time of a stationary discrete-time process above a high level in several examples: moving averages with non-negative... (Update)
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13: Mellin transforms and asymptotics: Harmonic sums - Flajolet, Gourdon et al. - 1995
13: An Introduction to Probability Theory and its Applications (context) - Feller - 1957
13: Central and local limit theorems applied to asymptotic enumeration (context) - Bender - 1973
BibTeX entry: (Update)
D. Aldous, Probability Approximations via the Poisson Clumping Heuristic, Springer, New York, 1989. http://citeseer.ist.psu.edu/aldous92probability.html More
@article{ aldous89probability,
author = "Aldous, D.",
title = "Probability Approximations Via The Poisson Clumping Heuristic, Springer",
journal = "NEW",
volume = "York",
pages = "1989",
year = "1989",
url = "citeseer.ist.psu.edu/aldous92probability.html" }
Citations (may not include all citations):57 A current view of random number generators (context) - Marsaglia - 1985
33 Implicit renewal theory and tails of solutions of random equ.. (context) - Goldie - 1991
18 Poisson approximations and the Chen-Stein method (context) - Arratia, Goldstein et al. - 1990
15 Two moments suffice for Poisson approximations: the Chen-Ste.. (context) - Arratia, Goldstein et al. - 1989
14 caching algorithms and self-organizing search (context) - Flajolet, Gardy et al. - 1987
13 The Erdos-Renyi strong law for pattern-matching with a given.. (context) - Arratia, Waterman - 1989
12 Brownian motion with a parabolic drift and Airy functions (context) - Groeneboom - 1989
11 Recent progress on the small parameter exit problem (context) - Day - 1987
11 Extremal properties of shot noise processes (context) - Hsing, Teugels - 1989
8 The harmonic mean formula for probabilities of unions: Appli.. (context) - Aldous - 1989 ACM
8 Sojourns and Extremes of Stochastic Processes (context) - Berman - 1992
6 Extrema and Related Topics for General Gaussian Processes (context) - Adler, to - 1990
6 for coin-tossing and sequence-matching (context) - Arratia, Gordon et al. - 1990
5 On non-increase of Brownian motion (context) - Burdzy - 1990
5 Methods for studying coincidences (context) - Diaconis, Mosteller - 1989
5 Covering problems for Markov chains (context) - Matthews - 1988
5 Measuring close approaches on a Brownian path (context) - Perkins, Taylor - 1988
4 Some applications of the Stein-Chen method for proving Poiss.. (context) - Barbour, Holst - 1989
4 Approximations and bounds for the distribution of the scan s.. (context) - Glaz - 1989
3 On extremal theory for stationary processes (context) - Albin - 1990
2 Extreme-value theory for dependent sequences via the Stein-C.. (context) - Smith - 1988
2 PhD thesis (context) - Sun, thesis - 1989
2 Stein's method in a two-dimensional coverage problem (context) - Aldous - 1989
1 Asymptotic distribution of the Normal sample range (context) - Matthews, Rukhin - 1991
1 Stationary self-similar extremal processes (context) - O'Brien, Torfs et al. - 1989
1 Weak laws for the increments of Wiener processes (context) - Deheuvels, Revesz - 1988
1 Asymptotic approximations for Brownian motion boundary hitti.. (context) - Roberts - 1991
1 Maxima and exceedences of stationary Markov chains (context) - Rootzen - 1988
1 High-level exceedences of regenerative and semistationary pr.. (context) - Serfozo - 1980
1 On extremal theory for differentiable stationary stochastic .. (context) - Albin - 1990
1 optimal solution to some problems not only on graphs (context) - Szpankowski - 1989
1 Poisson approximation in occupancy problems (context) - Barbour, Holst et al. - 1988
1 Sample path behavior of Ø 2 surfaces at extrema (context) - Aronowich, Adler - 1988
1 Poisson approximation with the Stein-Chen method and couplin.. (context) - Barbour, Holst et al. - 1988
1 The collector's problem with group drawings (context) - Stadje - 1990
1 Random walk in random environment: A counterexample (context) - Bramson, Durrett - 1988
1 the exceedence point process for a stationary sequence (context) - Hsing, Husler et al. - 1988
1 Extreme values of queue lengths in M=G=1 and GI=M=1 systems (context) - Serfozo - 1988
1 Asymptotic crossing rate for stationary Gaussian vector proc.. (context) - Breitung - 1988
1 Rates of Poisson convergence for some coverage and urn probl.. (context) - Holst, Kennedy et al. - 1988
1 Extreme values and high boundary crossings of locally statio.. (context) - Husler - 1990
1 Extreme values of birth-and-deathg processes and queues (context) - Serfozo - 1988
1 Lecture Notes in Statistics (context) - Husler, Reiss et al. - 1989
1 Percentage points of likelihood ratio tests for threshold au.. (context) - Chan - 1990
1 A limit theorem for probabilities related to the random bomb.. (context) - Isaac - 1987
1 Excursions of the Trajectories of Random Processes (context) - Tikhonov, Khimenko - 1987
1 A limit theorem on the number of overlapping appearances of .. (context) - Chrysaphinou, Papastavridis - 1988
1 processes with dependent components with applications to env.. (context) - Lindgren, for - 1989
1 Objects arranged randomly in space: an accessible theory (context) - Cowan - 1989
1 Extreme values: Theory and technical examples (context) - Lindgren, Rootzen - 1987
1 Poisson approximation using the Stein-Chen method and coupli.. (context) - Holst, Janson - 1988
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The Percolation Process on a Tree Where Infinite Clusters are.. - Aldous (1999) (Correct)
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