Effective dimension of points visited by Brownian motion
نویسندگان
چکیده
We consider the individual points on a Martin-Löf random path of Brownian motion. We show (1) that Khintchine’s law of the iterated logarithm holds at almost all points; and (2) there exist points (besides the trivial example of the origin) having effective dimension < 1. The proof of (1) amounts essentially to showing for almost all times t, the path f is random relative to t and the dimension of (t, f(t)) is 2.
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ورودعنوان ژورنال:
- Theor. Comput. Sci.
دوره 410 شماره
صفحات -
تاریخ انتشار 2009