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| I.I.D. STATISTICAL CONTRACTION OPERATORS AND STATISTICALLY SELF-SIMILAR SETS |
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Citation： |
HU Dihe.I.I.D. STATISTICAL CONTRACTION OPERATORS AND STATISTICALLY SELF-SIMILAR SETS[J].Chinese Annals of Mathematics B,2002,23(4):461~468 |
| Page view： 1039
Net amount： 635 |
Authors： |
HU Dihe; |
Foundation： |
Project supported by the National Natural Science Foundation of China, the Doctoral Progamme Foundation of China and the Foundation of Wuhan University. |
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| Abstract： |
I.i.d. random sequence is the simplest but very basic one in stochastic processes, and statistically self-similar set is the simplest but very basic one in random recursive sets in the theory of random fractal. Is there any relation between i.i.d. random sequence and statistically self-similar set? This paper gives a basic theorem which tells us that the random recursive set generated by a collection of i.i.d. statistical contraction operators is always a statistically self-similar set. |
Keywords： |
Hausdorff metric, Statistical contraction operator, Statistically self-similar set, Statistically self-similar measure |
Classification： |
60G55 |
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