Phys. Rev. E 63, 031109 (2001) [5 pages]Simple model of a random walk with arbitrarily long memoryReceived 23 July 2000; published 26 February 2001 We present a generalization of the persistent random-walk model in which the step at time n depends on the state of the step at time n-T, for arbitrary T. This gives rise to arbitrarily long memory effects, yet by an appropriate transformation the model is tractable by essentially the same techniques applicable to the usual persistent random-walk problem. We apply our results to the specific case of delayed “step” persistence, and analyze its asymptotic statistical properties. © 2001 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevE.63.031109
DOI:
10.1103/PhysRevE.63.031109
PACS:
05.40.Fb
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