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Vietnam
Journal of Mathematics 38:1 (2010) 2734

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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