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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 |
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Pham Van Chung and Nguyen Huu Bao |
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Abstract. Let us consider the composed random variable (r.v) $\eta=\sum_{k=1}^{\nu}\xi_k$ where $\xi_1,\xi_2,...$ are i.i.d r.vs and $\nu$ is positive $r.v$, independent of all $\xi_k$. In [1, 2], we gave some characterizations of the distribution function of $\eta$. In this paper, we give another characteristic function of $\eta$ satisfying some differential equations and prove the stabilities of those theorems. |
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2000 Mathematics Subject Classification: 60E10, 62H05, 62H15, 62HO5, 62H15. |
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Keywords: Characterization theorem; stability of characterization, stability estimation, probabilitic metric. |
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Vietnam Academy of Science and Technology
& Vietnamese Mathematical Society © Copyright 2009 Vietnam Journal of Mathematics. All rights reserved. |