Exist time and Green function of cone for symmetric stable processes

• Autorzy: Kulczycki T.
• Języki publikacji: EN

Abstrakty

EN

We obtain estimates of the harmonic measure and the expectation of the exit time of a bounded cone for symmetric α-stable processes X_t in R^d (α ϵ (0, 2), d ≥ 3). This enables us to study the asymptotic behaviour of the corresponding Green function of both bounded and unbounded cones. We also apply our estimates to the problem concerning the exit time τ_v of the process X_t from the unbounded cone V of angle λ ϵ (0, π/2). We namely obtain upper and lower bounds for the constant p₀ = p₀ (d, α, λ) such that for all x ϵ V we have E^x (τ^p_V) < ∞ for 0 ≤ p < p₀ and E^x (τ^p_V) = ∞ for p > p₀.

Słowa kluczowe

EN

symmetric stable process; harmonic measure; Green function; exit time; cone

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 1999
• Tom: Vol. 19, Fasc. 2
• Strony: 337--374
• Opis fizyczny: Bibliogr. 19 poz.

Twórcy

autor

Kulczycki T.

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

Bibliografia

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