Exist time and Green function of cone for symmetric stable processes

We obtain estimates of the harmonic measure and the expectation of the exit time of a bounded cone for symmetric α-stable processes Xt in Rd (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 τv of the process Xt 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 Ex (τpV) < ∞ for 0 ≤ p < p0 and Ex (τpV) = ∞ for p > p0.