Will a process with mean step 0 cross every bound infinitely often?

Asked Jun 04 '15 at 14:55

Active Jun 04 '15 at 16:09

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Take a discrete time process with mean step size 0. The steps will take values > ε with positive probability.

It seems intuitive that, for any bound, the process will cross the bound infinitely many times. Does anyone know of a result that says this?

edited Jun 04 '15 at 16:09

asked Jun 04 '15 at 14:55

firepanda

Suppose all steps are even. Then you never hit odd values. – GEdgar Jun 04 '15 at 15:04
Oops sorry. I meant cross every bound i.o. I was getting it confused with Brownian motion which does hit every point. – firepanda Jun 04 '15 at 16:10

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