A.D.BARBOUR and L. HOLST. Some applications of the Stein-Chen method for proving Poisson convergence. Advances in Applied Probability, 21:74--90, 1989. Home/Search Document Not in Database Summary Related Articles Check |
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Articles Sur Les Modèles D'urnes - Danièle Gardy (Correct)
....de Weiss en 1958 [46] puis de R enyi en 1962 [38] Holst pr esente dans un article de 1986 [16] une vision unifi ee de diff erents probl emes d allocation al eatoire, li ee a des temps d arret et a des statistiques d ordre sur une suite de processus de Poisson. L article de Barbour et Holst [1] pr esente une m ethode g en erale pour etudier une v.a. W obtenue comme somme de v.a. de Bernoulli. Le but est de montrer que W converge vers une loi de Poisson; pour cela une approche possible peut etre de borner la distance en variation entre W et une v.a. suivant une loi de Poisson de meme ....
....s int eresse au nombre d urnes ayant r boules, et consid ere, en sus du mod ele classique, le cas o u les urnes sont de taille born ee k; il donne les distributions, les fonctions caract eristiques ou des moments, et les moments. 2. 3 Lois non uniformes L article d ej a cit e de Barbour et Holst [1] s applique en particulier au cas d une loi de probabilit e non uniforme sur les urnes. Tikhomirova et Chistyakov [42] etudient un sch ema d allocation introduit dans [30] D apr es ce que je comprends du mod ele (il faudrait l article original, qui n est apparemment pas traduit. les urnes ....
A.D.BARBOUR and L. HOLST. Some applications of the Stein-Chen method for proving Poisson convergence. Advances in Applied Probability, 21:74--90, 1989.
Inequalities for Rare Events in Time-Reversible Markov Chains II - Aldous, Brown (1993) (9 citations) (Correct)
....Over the last five years it has become clear that Stein s method for approximating distributions of dependent sums is useful when the summands (loosely speaking) have either much combinatorial symmetry or essentially finite range dependence . See Arratia et al. [3, 4] and Barbour et al. [6, 7] for Poisson approximations involving such sums. It is not yet clear whether the method has substantially wider scope. Bluntly, this paper indicates how far one can get in this particular problem without having a new idea about implementing Stein s method. We regard the problem posed here as a ....
.... maximal correlation property of stationary reversible Markov chains. Lemma 4 exp( Gammat= maxfcor(Z 1 ; Z 2 ) Z 1 2 F(X s ; s 0) Z 2 2 F(X s ; s t)g = max h;g cor(h(X 0 ) g(X t ) The final ingredient is the following implementation of Stein s method given by Barbour and Holst [6] Theorem 2.1. Write jj Delta jj TV for total variation distance between distributions: jj Gamma jj TV = sup D j (D) Gamma (D)j: Proposition 5 Let (B i ; 1 i k) be events. Let N = P k i=1 1 B i count how many of these events occur. Let = EN = P i P (B i ) For each i let N ....
A.D. Barbour and L. Holst. Some applications of the Stein-Chen method for proving Poisson convergence. Adv. in Appl. Probab., 21:74--90, 1989.
Probability Approximations via the Poisson Clumping Heuristic: An .. - Aldous (1992) (73 citations) (Correct)
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A.D. Barbour and L. Holst. Some applications of the Stein-Chen method for proving Poisson approximation. J. Appl. Prob., 21:74--90, 1989.
On Poisson Approximation To The Partial Sum Process Of A Markov.. - Aihua (Correct)
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A. D. Barbour and L. Holst, Some applications of the Stein-Chen method for proving Poisson convergence 21 (1989), Adv. Appl. Prob., 74-90.
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