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Vietnam Journal of Mathematics 38:1 (2010) 27-34  

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

Nguyen Huu Bao and Do Lan

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(F_X; F_Y) = min_{T > 0} max{sup_|t|>T |φ_X(t) – φ_Y(t)|; 1/T}

for two distribution functions F_X; F_Y of two random variables X, Y and their corresponding characteristic functions φ_X(t) and φ_Y(t), eventhough when the condition in Theorem 2.1 in [1] is not satisfied.

2000 Mathematics Subject Classification: 60E10, 62H05, 62H15, 62H05, 62H15.

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

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Published by Springer since January 2013