On the Hausdorff dimension of the intersection of the range of a stable process with a Borel set
β Scribed by John Hawkes
- Publisher
- Springer
- Year
- 1971
- Tongue
- English
- Weight
- 542 KB
- Volume
- 19
- Category
- Article
- ISSN
- 1432-2064
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π SIMILAR VOLUMES
proved that for 0 \* 1 the set where W$(t) is a standard Wiener process. A corresponding result is obtained when W$ is replaced by a two-parameter Wiener process.
We give a lower estimate of the Hausdorff dimension for Cantor-like sets which are obtained by an overlapping Moran-like construction.
In this paper we improve the construction of Goto (1993) to obtain the Main Theorem: Let n, m and k be arbitrary integers such that 0 < m < n -1 3 1 and m < k < min{2m, n -1). Then there exists a point set Xk,, in Euclidean n-space IR" such that (i) pdimX& = m and dimXk,, = k, (ii) pdim(X& n H) = m