%0 Journal Article
%T The Hausdorff Dimension for a Class of Generalized Random Fractals<br>一类推广的随机分形的 Hausdorff维数
%A Zhuang Yan
%A Dai Chaoshou
%A <br>庄艳
%A 戴朝寿
%J 数学物理学报(A辑)
%D 2008
%I 
%X In this paper, a class of generalized random recursive construction with finite memory in Euclidean $d$-space is researched. For each $\beta\geq 0$, a function $\Psi(\beta)$ assiociated with the construction is introduced and a random measure $\mu_{\omega}$ is constructed. That the Hausdorff dimension of the random limit set $K(\omega)$ generated by the above construction is equal to $\alpha:=\inf\{\beta:\Psi(\beta)\leq1\}$ is proved.
%K Hausdorff dimensionzz
%K Random constructionzz
%K Supermartingalezz
%K Extension of measurezz
%K Random measurezz
%K Local dimensionzz<br>Hausdorff维数
%K 随机结构
%K 上鞅
%K 测度的扩张
%K 随机测度
%K 局部维数.
%K 类推
%K 随机分形
%K Hausdorff
%K 维数
%K Fractals
%K Random
%K Generalized
%K Class
%K 随机集
%K 随机测度
%K 构造
%K 函数
%K 结构
%K 递归模型
%K 有限记忆
%K 研究
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=6E709DC38FA1D09A4B578DD0906875B5B44D4D294832BB8E&cid=37F46C35E03B4B86&jid=4DB553CDB5F521D8C921082E5C95EC80&aid=3285BAE9EE61A19BB241C863BD117CBB&yid=67289AFF6305E306&vid=D3E34374A0D77D7F&iid=0B39A22176CE99FB&sid=C812B90E96151014&eid=1D01216AD76577EC&journal_id=1003-3998&journal_name=数学物理学报(A辑)&referenced_num=0&reference_num=17