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First passage times for correlated random walks and some generalizations

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Abstract

It is generally difficult to solve Fokker-Planck equations in the presence of absorbing boundaries when both spatial and momentum coordinates appear in the boundary conditions. In this note we analyze a simple, exactly solvable model of the correlated random walk and its continuum analogue. It is shown that one can solve for the moments recursively in one dimension in exact analogy with first passage problems for the Fokker-Planck equation, although the boundary conditions are somewhat more complicated. Further generalizations are suggested to multistate random walks.

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Authors and Affiliations

  1. Physical Sciences Laboratory, Division of Computer Research & Technology, National Institutes of Health, 20205, Bethesda, Maryland

    George H. Weiss

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  1. George H. Weiss
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Weiss, G.H. First passage times for correlated random walks and some generalizations. J Stat Phys 37, 325–330 (1984). https://doi.org/10.1007/BF01011837

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  • DOI: https://doi.org/10.1007/BF01011837

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