Leike, Jan; Hutter, Marcus
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
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