Multiple points of dilation-stable Levy processes

• 成果类型: Article
• 署名作者: Shieh, NR
• 署名单位: National Taiwan University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 1998
• 页码: 1341-1355
• 关键词: sample paths

摘要

Let X be a symmetric Levy process in R-d, d = 2, 3. We assume that X has independent alpha(j)-stable components, 1 < alpha(d) less than or equal to ... less than or equal to alpha(1) < 2 (a process with stable components, by Pruitt and Taylor), or more generally that X is d-dimensionally self-similar with similarity exponents H-j, H-j = 1/alpha(j) (a dilation-stable process, by Kunita). Let a given integer k greater than or equal to 2 be such that k(H - 1) < H, H = Sigma(j=1)(d) H-j. We prove that the set of k-multiple points E-k is almost surely of Hausdorff dimension dim E-k = min ( k - (k - 1)H/H-1, d - k(H - 1)/H-d). In the stable components case, the above formula was proved by Hendricks for d = 2 and was suspected by him for d = 3.