Covering the whole space with Poisson random balls
19 pages
English

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Covering the whole space with Poisson random balls

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19 pages
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Description

1COVERING Rd WITH POISSON RANDOM BALLS Anne Estrade (MAP5 and ANR-09-BLAN-0029 mataim) joint work with Hermine Biermé (MAP5) Stoch. Geom. Lille - April 2011

  • lebesgue measure

  • ?vd ∫

  • poisson property

  • covering rd

  • still valid

  • balls

  • boolean model

  • open random


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Informations

Publié par
Nombre de lectures 20
Langue English

Extrait

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L L
p := P(B(0,1)∩Σ =∅)
L
= P(B(0,1)∩Σ =∅ B(0,1)⊂ Σ)
L
= P(B(0,1)∩Σ =∅ B(0,1)⊂ Σ )
L H
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Z Z
1 1
d−1 d−1
u exp v r (r−u)μ(dr) du = +∞
d
0 u
d = 1
atcoShepp'svtheerage(conTheoremcondition:asHighGEFREQUENCYwithHIGHoundary2isVERAsameW-9(frequency-AND)LOKahane'sCOvexsetsofa:bTheinsteadnecessaryballs)Remarkd
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ε> 0
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ε y∈/Σ
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H,≥ε
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R
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−κ d
ε
E(m ) =e κ =v r μ(dr)
ε ε d
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ε
E(m )≤...≤Ie I ∈ (0,+∞)
ε
2
E(m )
ε
−1
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ε
2
E(m )
ε
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