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Vietnam Journal of Mathematics 35:3(2007) 255-265

 On the Characterizations and Their Stabilities of the Composed Random Variables by Constant-Regression

Pham Van Chung and Nguyen Huu Bao

Abstract.  Let us consider the composed random variable (r.v) where ξ_1, ξ_2,... are i.i.d r.vs and ν is positive r.v, independent of all ξ_k. In [1, 2], we gave some characterizations of the distribution function of η. In this paper, we give another characteristic function of η satisfying some differential equations and prove the stabilities of those theorems.

2000 Mathematics Subject Classification: 60E10, 62H05, 62H15, 62HO5, 62H15.

Keywords: Characterization theorem; stability of characterization, stability estimation, probabilitic metric.

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