Censoring Estimators Of A Positive Tail Index And The Viscosity Solution Of Degenerate Elliptic Equation

In the first part of this paper, a kind of location invariant Hill-type estimators:denoted was proposed, whereandMain results are briefly as follows:Theorem 1 Let k(n) and k₀(k) be intermediate sequence,such that k =k(n) →∞, k₀ = k₀(k)→∞, k/n→∞,as n→∞ and U(t) ∈ RV_γ , thenTheorem 2 Suppose that there exists A(t) →0, with constant sign near infinity and different from zero, such thatwhere Z_n is asmptotically standard normal,andIn the second part, the probpabilistic solution of Dirichlet problem for the linear degenerate elliptic equation was studied. The unique viscosity of the degenerate elliptic equation was derived.