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Behaviors of generalized random walks. The model and its evaluations

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  • Hara, Hiroaki
  • Sato, Hiroshi

Abstract

Behaviors of the generalized random walks (GRW) are directly studied by using computer. The GRW have a non-linear term yielding a non-Markovian character. The non-Markovian character represents memory effects in the processes through the jumping probabilities P̃αN(m|m−α1) between sites m−α1 and m at Nth step. In the computations, the probability that the walker starting at origin arrives site m after N steps, W(m, N), is plotted by varying three parameters. The three parameters specify the jumping probabilities and the memory effects. Furthermore, the P̃αN(m|m−α1)'s are numerically evaluated from the W(m, N). The W(m, N) is compared with the corresponding probability density w(x, t) obtained by taking the continuous limit.

Suggested Citation

  • Hara, Hiroaki & Sato, Hiroshi, 1983. "Behaviors of generalized random walks. The model and its evaluations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 120(1), pages 351-366.
    • Handle: RePEc:eee:phsmap:v:120:y:1983:i:1:p:351-366
    DOI: 10.1016/0378-4371(83)90283-2
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