Displaying similar documents to “A general Choquet–Deny theorem for nilpotent groups”

Events of Borel Sets, Construction of Borel Sets and Random Variables for Stochastic Finance

Peter Jaeger (2014)

Formalized Mathematics

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We consider special events of Borel sets with the aim to prove, that the set of the irrational numbers is an event of the Borel sets. The set of the natural numbers, the set of the integer numbers and the set of the rational numbers are countable, so we can use the literature [10] (pp. 78-81) as a basis for the similar construction of the proof. Next we prove, that different sets can construct the Borel sets [16] (pp. 9-10). Literature [16] (pp. 9-10) and [11] (pp. 11-12) gives an overview,...

Most random walks on nilpotent groups are mixing

R. Rębowski (1992)

Annales Polonici Mathematici

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Let G be a second countable locally compact nilpotent group. It is shown that for every norm completely mixing (n.c.m.) random walk μ, αμ + (1-α)ν is n.c.m. for 0 < α ≤ 1, ν ∈ P(G). In particular, a generic stochastic convolution operator on G is n.c.m.

Integral representation for a class of multiply superharmonic functions

Kohur Gowrisankaran (1973)

Annales de l'institut Fourier

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Let Ω 1 , ... , Ω n be harmonic spaces of Brelot with countable base of completely determining domains. The elements of a subcone C of the cone of positive n -superharmonic functions in Ω 1 × ... × Ω n is shown to have an integral representation with the aid of Radon measures on the extreme elements belonging to a compact base of C . The extreme elements are shown to be the product of extreme superharmonic functions on the component spaces and the measure representing each element is shown to be unique. Necessary...