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Analytic study of the effect of persistence on a one-dimensional biased random walk

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  • Pottier, Noëlle

Abstract

An analytic study of a one-dimensional biased random walk with correlations between nearest-neighbour steps is presented, both in a lattice model and in its continuous version. First, the treatment of the unbiased problem is recalled and the effect of correlations on the diffusion coefficient is discussed. Then the study is extended to the biased case. The problem is then completely determined by two independent parameters, the degree of correlations in the motion on the one hand and the value of the bias on the other. Both the velocity of the particle and its diffusion coefficient are computed. As a result, the velocity as well as the diffusion coefficient are enhanced when there are positive correlations (qualified as persistence) in the motion, and reduced in the opposite case.

Suggested Citation

  • Pottier, Noëlle, 1996. "Analytic study of the effect of persistence on a one-dimensional biased random walk," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 230(3), pages 563-576.
    • Handle: RePEc:eee:phsmap:v:230:y:1996:i:3:p:563-576
    DOI: 10.1016/0378-4371(96)00075-1
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    Cited by:

    1. Rodriguez-Horta, E. & Estevez-Rams, E. & Lora-Serrano, R. & Fernández, B. Aragón, 2016. "Correlated biased random walk with latency in one and two dimensions: Asserting patterned and unpredictable movement," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 458(C), pages 303-312.
    2. Vallois, Pierre & Tapiero, Charles S., 2007. "Memory-based persistence in a counting random walk process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 386(1), pages 303-317.
    3. Vallois, Pierre & Tapiero, Charles S., 2009. "A claims persistence process and insurance," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 367-373, June.

    More about this item

    Keywords

    Fluctuation phenomena; Random walks;

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