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Say I have a process starting from 0, and last for 100 steps, each step either moves up or down by one unit, within the boundary -10 and 10.

My understanding is that since this is a martingale, the expected hitting time would be 100, but how to calculate the local time aka how many times it would hit the boundaries within the 100 steps?

Thanks!

butterbetter
  • 351
  • Why not just creating the proper probability sum (exactly 10 + exactly 11 +... where the number signifies the boundary hitting) for up (X2 and you add the down) and than multiply it by 100 - the number of attempts. – Moti Apr 01 '15 at 04:41

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