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Indefinitely oscillating martingales

Leike, Jan; Hutter, Marcus

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 of the...[Show more]

CollectionsANU Research Publications
Date published: 2014
Type: Conference paper
URI: http://hdl.handle.net/1885/53518
Source: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) Volume 8776
DOI: 10.1007/978-3-319-11662-4_23

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