On the asymptotic behavior of some Algorithms
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(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. On the asymptotic behavior of some Algorithms Philippe Robert. N° 5421 Deembre 2004. N 0249-6399. ISRN INRIA/RR--5421--FR+ENG. Thème COM. apport de recherche.
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(70)
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(122) ! n−1
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(124) X
(125)
(126) n a Gn−k ≥ x − P (H ≥ x)
(127) = 0. lim sup
(128) P n→+∞ x≥0
(129)
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(132) u/.
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(138) +. & ! &'!#.
(139) /#.0! & +. H. +. ,. X X E uL(t) = E un (1 − u) 1{L(t)≤n} = un (1 − u) P (L(t) ≤ n) #*
(140). n≥0. P (L(t) ≤ n) = P (G1 + · · · + Gn ≥ t) ,. E [exp (−λL(t))] =. X. e. −λn. n≥0. 1−e.
(141) : ;"'3 &<=#8'3?>3
(142) *
(143) #8
(144) A@ B*C?D7 >
(145) 7
(146) E
(147) 8FG. E [exp (−λL(t))] =. X. n≥0. JKJ=LNMO.P8Q/R. a = 1/2. . n≥0. ' 12 .
(148) * ). −λ. +. . P a. ' . n. "'3. n−1 X i=0. , +. . n ≥ 1 45. t.
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(150) 8 9 &
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(152) *1. n. !. Gn−i ≥ a t ,. '6
(153) H &'!I; ,. e−λn 1 − e−λ P (H ≥ an t) + o(1),. λ > 0.. +. &' .
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(155) D ¦ F
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(159) [E\kYyUn]Z>\[k\kmTG`c SVUW[lmTQa H. . n. OQPMqROTS.
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(214) Unité de recherche INRIA Rocquencourt Domaine de Voluceau - Rocquencourt - BP 105 - 78153 Le Chesnay Cedex (France) Unité de recherche INRIA Futurs : Parc Club Orsay Université - ZAC des Vignes 4, rue Jacques Monod - 91893 ORSAY Cedex (France) Unité de recherche INRIA Lorraine : LORIA, Technopôle de Nancy-Brabois - Campus scientifique 615, rue du Jardin Botanique - BP 101 - 54602 Villers-lès-Nancy Cedex (France) Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu - 35042 Rennes Cedex (France) Unité de recherche INRIA Rhône-Alpes : 655, avenue de l’Europe - 38334 Montbonnot Saint-Ismier (France) Unité de recherche INRIA Sophia Antipolis : 2004, route des Lucioles - BP 93 - 06902 Sophia Antipolis Cedex (France). Éditeur INRIA - Domaine de Voluceau - Rocquencourt, BP 105 - 78153 Le Chesnay Cedex (France).
(215). . ISSN 0249-6399.
(216)
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