Geometry of multivariate stable laws

Ilya Molchanov

Description

Geometry of multivariate stable laws Ilya Molchanov University of Bern, Switzerland 1

• minkowski sums


• exponent ?


• central symmetry


• convex geometry


• notation s?s


• symmetric stable


• centrally symmetric

Sujets

• Point reflection
• Convex geometry

Informations

• Publié par: profil-urra-2012
• Nombre de lectures: 10
• Langue: English

Extrait

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Realisability problems

Ilya Molchanov

University of Bern, Switzerland

Available from Arxiv: math.PR/1102.1950

joint work with Raphael Lachieze-Rey

University of Lille and University of Luxembourg

1

Eg(ξ)

g

og7→Φ(g) =Eg(ξ) is a linear functional

o What if Φ(g) is given only forsomefunctions g ?

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ξ is a random element in space X

o

Distribution of ξ is uniquely specied by

o

2

Expected functionals

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o

ξ is not uniquely specied.

ξ ?

3

o

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o normalisedfunctional on vector lattice E is the Lebesgue integral w.r.t. probability measure, i.e. theexpectation.

o Idea: positively extend Φ from functions g∈G to a wider family of functions v∈E such that E is a vector lattice.

o If g≥0 , then Φ(g) =Eg(ξ)≥0 .

Positivity

4

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