Fractal properties of the randomstring processes
نویسندگان
چکیده
where Ẇ (x, t) is an R-valued space-time white noise. Mueller and Tribe (2002) have proved necessary and sufficient conditions for the R-valued process {ut(x) : t ≥ 0, x ∈ R} to hit points and to have double points. In this paper, we continue their research by determining the Hausdorff and packing dimensions of the level sets and the sets of double times of the random string process {ut(x) : t ≥ 0, x ∈ R}. We also consider the Hausdorff and packing dimensions of the range and graph of the string.
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