Potential theory of hyperbolic Brownian motion in tube domains

• Autorzy: Grzegorz Serafin
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 60J60: Diffusion processes
• 60J65: Brownian motion

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2014
• Tom: 135
• Numer: 1
• Strony: 27-52

Daty

wydano

2014

Twórcy

autor

Grzegorz Serafin

• Institute of Mathematics and Computer Science, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

Identyfikatory

DOI

10.4064/cm135-1-3