Acta mathematica scientia,Series A ›› 2001, Vol. 21 ›› Issue (4): 443-452.
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YU Jing-Hu
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国家自然科学基金资助项目
Abstract:
定义了一类广泛的随机自仿射集，得到了此类集合的Ｈａｕｓｄｏｒｆｆ维数估计．此前的随机自相似（包括Ｇｒａｆ，Ｍａｕｌｄｉｎ与Ｆａｌｃｏｎｅｒ等定义的随机自相似情形）和Ｆａｌｃｏｎｅｒ定义的（严格）自仿射以及作者定义的μ统计自仿射情形均成为该文结果的特例．
Key words: 自仿射集, μ统计自仿射集, 随机自仿射集, Ｈａｕｓｄｏｒｆｆ维数, 奇异值函数．
CLC Number:
YU Jing-Hu. The Estimates for the Hausdorff Dimension of Random Self-Affine Fractals[J].Acta mathematica scientia,Series A, 2001, 21(4): 443-452.
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http://121.43.60.238/sxwlxbA/EN/Y2001/V21/I4/443
１ ＡｔｈｒｅｇａＫＢ，ＮｅｙＰＥ．ＢｒａｎｃｈｉｎｇＰｒｏｃｅｓｓｅｓ．Ｂｅｒｌｉｎ：Ｓｐｒｉｎｇｅｒ，１９７２ ２ ＦａｌｃｏｎｅｒＫＪ．Ｒａｎｄｏｍｆｒａｃｔａｌｓ．ＭａｔｈＰｒｏｃＣｏｍｂＰｈｉｌｏｓＳｏｃ，１９９６，１００：５５９－５８２ ３ ＦａｌｃｏｎｅｒＫＪ．ＴｈｅＨａｕｓｄｏｒｆｆｄｉｍｅｎｓｉｏｎｏｆｓｅｌｆａｆｆｉｎｅｆｒａｃｔａｌｓ．ＭａｔｈＰｒｏｃＣｏｍｂＰｈｉｌＳｏｃ，１９８８，１０３：３３９－３５９ ４ ＦａｌｃｏｎｅｒＫＪ．ＴｈｅｄｉｍｅｎｓｉｏｎｏｆｓｅｌｆａｆｆｉｎｅｆｒａｃｔａｌｓＩＩ．ＭａｔｈＰｒｏｃＣｏｍｂＳｏｃ，１９９２，１１１：１６９－１７９ ５ ＧｒａｆＳ．Ｓｔａｔｉｓｔｉｃａｌｌｙｓｅｌｆｓｉｍｉｌａｒｆｒａｃｔａｌｓ．ＰｒｏｂＴｈＲｅｌＦｉｅｌｄｓ，１９８７，７４：３５７－３９２ ６ ＧａｔｚｏｕｒａｓＤ，ＬａｌｌｅｙＳＰ．Ｓｔａｔｉｓｔｉｃａｌｌｙｓｅｌｆａｆｆｉｎｅｓｅｔｓ：ＨａｕｓｄｏｒｆｆａｎｄＢｏｘｉｎｇｄｉｍｅｎｓｉｏｎ．ＪｏｆＴｈＰｒｏｂ，１９９４，７：４３７－４６８ ７ ＨｕｔｃｈｉｎｓｏｎＪＥ．Ｆｒａｃｔａｌｓａｎｄｓｅｌｆｓｉｍｉｌａｒｉｔｙ．ＩｎｄｉａｎａＵｎｉｖＭａｔｈＪ，１９８１，３０：７１３－７４７ ８ 胡迪鹤．随机分形引论．武汉：武汉大学出版社，１９９５ ９ ＭａｕｌｄｉｎＲＤ，ＷｉｌｌｉａｍｓＳＣ．Ｒａｎｄｏｍｒｅｃｕｓｉｖｅｃｏｎｓｔｒｕｃｔｉｏｎｓ：ａｓｙｍｐｔｏｔｉｃｇｅｏｍｅｔｒｉｃａｎｄｔｏｐｏｌｏｇｉｃａｌｐｒｏｐｅｒｔｉｅｓ．Ｔｒａｎｓ ＡｍｅｒＭａｔｈＳｏｃ，１９８６，２９５：３２５－３４６ １０ ＭｃｍｕｌｌｅｎＣ．ＴｈｅＨａｕｓｄｏｒｆｆｄｉｍｅｎｓｉｏｎｏｆｇｅｎｅｒａｌＳｉｐｅｒｐｉｎｓｋｉＣａｒｐｅｔｓ．ＮａｇｏｙａＭａｔｈＪ，１９８４，９６：１－９ １１ ＭｏｒａｎＰＡＰ．ＡｄｄｉｔｉｖｅｆｕｎｃｔｉｏｎｓｏｆｉｎｔｅｒｖａｌｓａｎｄＨａｕｓｄｏｒｆｆｍｅａｓｕｒｅ．ＰｒｏｃＣａｍｂＰｈｉｌｏｓＳｏｃ，１９４６，４２：１５－２３ １２ 余旌胡．μ统计自仿射集的Ｈａｕｓｄｏｒｆｆ维数估计．数学年刊，Ａ 辑，１９９９，２０（２）：２０３－２１２
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