Abstract
For each $a \in (0, \frac{1}{2})$, there exists a random measure $\beta_a$ which is supported on the set of points where two-dimensional Brownian motion spends $a$ units of local time. The measure $\beta_a$ is carried by a set which has Hausdorff dimension equal to $2 - a$. A Palm measure interpretation of $\beta_a$ is given.
Citation
Richard F. Bass. Krzysztof Burdzy. Davar Khoshnevisan. "Intersection Local Time for Points of Infinite Multiplicity." Ann. Probab. 22 (2) 566 - 625, April, 1994. https://doi.org/10.1214/aop/1176988722
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