A New Method to Estimate the Stable Degrees of Some Previous Stability Theorems Based on the Stability of the Differential Equations for Characteristic Functions

Authors: Nguyễn Hữu Bảo, Đỗ Lân,

http://www.math.ac.vn/publications/vjm/VJM_38/27.htm

Publisher, magazine: ,

Publication year: 2010

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Abstract

We reconsider two previous stability problems in [2, 3] and give other estimations of the stable degrees of these problems with the following metric: λ(FX; FY) = minT > 0 max{sup|t|>T |φX(t) – φY(t)|; 1/T} for two distribution functions FX; FY of two random variables X, Y and their corresponding characteristic functions φX(t) and φY(t), eventhough when the condition in Theorem 2.1 in [1] is not satisfied.

Tags: Characterization theorem, stability of characterization, stability estimation, probabilistic metric.