超α-对称稳定过程的局部灭绝性  

On the Local Extinction for the Supper α-Symmetric Stable Processes

作　　者：坚雄飞[1] 赵学雷[2] 

机构地区：[1]华南师范大学数学系,广州广东510631 [2]复旦大学数学研究所,上海200433

出　　处：《数学进展》2000年第4期345-353,共9页Advances in Mathematics（China）

基　　金：广东省自然科学基金!(NO.990444)

摘　　要：考虑初始测度为 Ｌｅｂｅｓｇｕｅ测度μ的超α－对称稳定（记为α－ＳＳ）过程，其分枝特征为■（ｘ，ｚ）＝－γ（ｘ）ｚ１＋β０（＜β≤－１）．本文研究这类超过程的局部灭绝性．运用纯分析的方法我们首先得到了局部灭绝的一个充分条件，借助这一条件，对较特殊的γ（ｘ）＝（１＋｜ｘ｜）θ（θ＜βｄ）；证明了与之联系的超α－ＳＳ过程存在局部灭绝的临界值 θ＊，同时给出它的一个上界 βｄ－ａ若 γ（ｘ）■ １；这意味着 ｄ≤－α，类似的结果可见于山．最后，我们针对γ（ｘ）无界的情形做了一些讨论．in this paper, we deal with the local extinction of super a-symmetric stable processes (denoted by super a-SS) with the branching characteristic ■(x, z) = -r(x)z1+β(0 < β <- 1) in Mp(Rd), and present a sufficient condition for its local extinction. Our result relies on the dimension of underly space and the chacteristic of the super or-SS processes. This result is also available to 700 which may be unbounded. For the case (x) 1, this equivalent to the condition that βd <- α) the similar result is established by Dawson in 1977. In particular, if r(x) = (1 + |x|)' with θ < βd, then we prove that there is a critical value θ*, which has an upper bound βd - a, and the related super α-SS processes is locally extinct if and only if θ 3 θ*.

关 键 词：局部灭绝 比较定理 超α-对称稳定过程 

分 类 号：O211.61[理学—概率论与数理统计]