Indefinitely Oscillating Martingales
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Description
We construct a class of nonnegative martingale processes that oscillate indefinitely with high probability. For these processes, we state a uniform rate of the number of oscillations for a given magnitude and show that this rate is asymptotically close to the theoretical upper bound. These bounds on probability and expectation of the number of upcrossings are compared to classical bounds from the martingale literature. We discuss two applications. First, our results imply that the limit...[Show more]
Collections | ANU Research Publications |
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Date published: | 2014-10 |
Type: | Conference paper |
URI: | http://hdl.handle.net/1885/14701 |
Book Title: | Algorithmic Learning Theory: 25th International Conference, ALT 2014, Bled, Slovenia, October 8-10, 2014. Proceedings |
DOI: | 10.1007/978-3-319-11662-4_23 |
Access Rights: | Open Access |
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File | Description | Size | Format | Image |
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Leike and Hutter Indefinitely Oscillating Martingales 2014.pdf | 374.02 kB | Adobe PDF |
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