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Potential theory of hyperbolic Brownian motion in tube domains

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Serafin G.

Colloquium Mathematicum

2014

tom 135

nr 1

27-52

Let X = {X(t); t ≥ 0} be the hyperbolic Brownian motion on the real hyperbolic space ℍⁿ = {x ∈ ℝⁿ:xₙ > 0}. We study the Green function and the Poisson kernel of tube domains of the form D × (0,∞)⊂ ℍⁿ, where D is any Lipschitz domain in $ℝ^{n-1}$. We show how to obtain formulas for these functions using analogous objects for the standard Brownian motion in $ℝ^{2n}$. We give formulas and uniform estimates for the set $D_a = {x ∈ ℍⁿ:x₁ ∈ (0,a)}$. The constants in the estimates depend only on the dimension of the space.

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1 Colloquium Mathematicum

1 Serafin G.

1 2014

Wyniki wyszukiwania

Potential theory of hyperbolic Brownian motion in tube domains