统计自相似集和测度的概率特征

Abstract

Abstract:

Ｉｎｔｈｉｓｐａｐｅｒ，ｗｅｈａｖｅｐｒｏｖｅｄｔｈａｔｔｈｅｓｔａｔｉｓｔｉｃａｌｌｙｓｅｌｆ-ｓｉｍｉｌａｒｓｅｔｉｓｇｅｎｅｒａｔｅｄｂｙａｃｏｌｌｅｃｔｉｏｎｏｆｒａｎｄｏｍｃｏｎｔｒａｃｔｉｏｎｏｐｅｒａｔｏｒｓ｛fσ，σ∈D｝，ｗｈｅｒｅ fσ ｉｓａｒａｎｄｏｍｅｌｅｍｅｎｔｓｆｒｏｍｐｒｏｂａｂｉｌｉｔｙｓｐａｃｅ（Ω，，P）ｔｏｃｏｎ（E），ａｎｄｃｏｎ（E）ｄｅｎｏｔｅｓａｌｌｃｏｎｔｒａｃｔｉｏｎｏｐｅｒａｔｏｒｓｆｒｏｍｃｏｍｐｌｅｔｅｓｅｐａｒａｂｌｅｍｅｔｒｉｃｓｐａｃｅEｔｏE．

Key words: Ｓｔａｔｉｓｔｉｃａｌｌｙｓｅｌｆｓｉｍｉｌａｒｓｅｔ, Ｓｔａｔｉｓｔｉｃａｌｌｙｓｅｌｆｓｉｍｉｌａｒｍｅａｓｕｒｅ, Ｒａｎｄｏｍｓｅｔ, Ｄｉｓｔｒｉｂｕｔｉｏｎ．

CLC Number:

　６０Ｇ

Hu Dihe. The Probability Character of Statistically Self-Similar Sets And Measures[J].Acta mathematica scientia,Series A, 1999, 19(3): 338-346.

Trendmd

References

１　ＨｕＤｉｈｅ．Ｔｈｅｃｏｎｓｔｒｕｃｔｉｏｎｏｆｓｔａｔｉｓｔｉｃａｌｌｙｒｅｃｕｒｓｉｖｅｓｅｔｓ．ＷｕｈａｎＵｎｉｖＪｏｆＮａｔＳｃｉ，１９９８，３（３）：２６５－２６９
２　ＨｕＤｉｈｅ．Ｔｈｅｃｌａｓｓｉｆｉｃａｔｉｏｎｏｆｓｔａｔｉｓｔｉｃａｌｌｙｒｅｃｕｒｓｉｖｅｓｅｔｓ．ＷｕｈａｎＵｎｉｖＪｏｆＮａｔＳｃｉ，１９９８，３（３）：２７０－２７６
３　ＢｉｌｌｉｎｇｓｌｅｙＰ．Ｃｏｎｖｅｒｇｅｎｃｅｏｆｐｒｏｂａｂｉｌｉｔｙｍｅａｓｕｒｅ，ＮｅｗＹｏｒｋ：ＪｏｈｎＷｉｌｅｙ＆ＳｏｎｃＩｎｃ，１９６８
４　ＧｒａｆＳ．Ｓｔａｔｉｓｔｉｃａｌｌｙｓｅｌｆｓｉｍｉｌａｒｆｒａｃｔａｌｓ．ＰｒｏｂＴｈＲｅｌＦｉｅｌｄｓ，１９８７，７４：３５７－３９２
５　ＭａｕｌｄｉｎＲＤ，ＷｉｌｌｉａｍｓＳＣ．Ｒａｎｄｏｍｒｅｃｕｒｓｉｖｅｃｏｎｓｔｒｕｃｔｉｏｎ：Ａｓｙｍｐｔｏｔｉｃｇｅｏｍｅｔｒｉｃａｎｄｔｏｐｏｌｏｇｉｃａｌｐｒｏｐｅｒｔｉｅｓ．ＴｒａｎｓＡｍｅｒＭａｔｈＳｏｃ，１９８６，２９５：３２５－３４６
６　ＦａｌｃｏｎｅｒＫＪ．ＴｈｅＨａｕｓｄｏｒｆｆｄｉｍｅｎｓｉｏｎｏｆｓｅｌｆａｆｆｉｎｅｆｒａｃｔａｌｓⅡ．ＭａｔｈＰｒｏｃＣａｍｂＰｈｉｌＳｏｃ，１９９２，１１１：１６９－１７９
７　ＨｕｔｃｈｉｎｓｏｎＪＥ．Ｆｒａｃｔａｌｓａｎｄｓｅｌｆｓｉｍｉｌａｒｉｔｙ．ＩｎｄｉａｎａＵｎｉｖＭａｔｈＪ，１９８１，３０：７１３－７４７

[1]	JIANG Chao. Local Tail Asymptotic Relations for the Stationary Waiting Time Distribution of \|GI/G/[STHZ]1[STBZ]/∞ Queueing System [J]. Acta mathematica scientia,Series A, 2004, 4(6): 752-757.
[2]	Qian Nengsheng. On the Renewal Theorem for Random Compact Convex Sets [J]. Acta mathematica scientia,Series A, 1998, 18(S1): 107-114.

The Probability Character of Statistically Self-Similar Sets And Measures

PDF (PC)

Abstract

Cite this article

share this article

References

Related Articles 2

Metrics

Comments

Recommended 10