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First passage time problems for a class of master equations with separable kernels

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  • Weiss, George H.
  • Szabo, Attila

Abstract

We discuss first passage time problems for a class of one-dimensional master equations with separable kernels. For this class of master equations the integral equation for first passage time moments can be transformed exactly into ordinary differential equations. When the separable kernel has only a single term the equation for the mean first passage time obtained is exactly that for simple diffusion. The boundary conditions, however, differ from those appropriate to simple diffusion. The equations for higher moments differ slightly from those for simple diffusion. Analysis is presented, of a generalization of a model of a random walk with long-range jumps first investigated by Lindenberg and Shuler. Since the equations can be solved exactly one can study the behavior of boundary conditions in the continuum limit. The generalization to a larger number of terms in the separable kernel leads to higher order equations for the first passage time moments. In each case, boundary conditions can be found directly from the original master equation.

Suggested Citation

  • Weiss, George H. & Szabo, Attila, 1983. "First passage time problems for a class of master equations with separable kernels," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 119(3), pages 569-579.
    • Handle: RePEc:eee:phsmap:v:119:y:1983:i:3:p:569-579
    DOI: 10.1016/0378-4371(83)90109-7
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    References listed on IDEAS

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    1. Schulten, Klaus & Schulten, Zan & Szabo, Attila, 1980. "Reactions governed by a binomial redistribution process—The ehrenfest urn problem," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 100(3), pages 599-614.
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    Cited by:

    1. Sandra H Dandach & Mustafa Khammash, 2010. "Analysis of Stochastic Strategies in Bacterial Competence: A Master Equation Approach," PLOS Computational Biology, Public Library of Science, vol. 6(11), pages 1-11, November.
    2. Denisov, S.I. & Bystrik, Yu.S., 2019. "Statistics of bounded processes driven by Poisson white noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 38-46.

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