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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(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.

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

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

 

 

 

 

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