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- W2962793793 abstract "Abstract Let N and M be positive integers satisfying 1≤ M ≤ N , and let 0< p 0 < p 1 < 1. Define a process {X n } n=0 ∞ on ℤ as follows. At each step, the process jumps either one step to the right or one step to the left, according to the following mechanism. For the first N steps, the process behaves like a random walk that jumps to the right with probability p 0 and to the left with probability 1- p 0 . At subsequent steps the jump mechanism is defined as follows: if at least M out of the N most recent jumps were to the right, then the probability of jumping to the right is p 1 ; however, if fewer than M out of the N most recent jumps were to the right then the probability of jumping to the right is p 0 . We calculate the speed of the process. Then we let N → ∞ and M / N → r ∈[0,1], and calculate the limiting speed. More generally, we consider the above questions for a random walk with a finite number l of threshold levels, ( M i , p i ) i =1 l , above the pre-threshold level p 0 , as well as for one model with l = N such thresholds." @default.
- W2962793793 created "2019-07-30" @default.
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- W2962793793 date "2016-03-01" @default.
- W2962793793 modified "2023-10-16" @default.
- W2962793793 title "The speed of a random walk excited by its recent history" @default.
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- W2962793793 doi "https://doi.org/10.1017/apr.2015.14" @default.
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