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Discrete random walk representations for continuum stochastic dynamics

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  • Vlad, Marcel Ovidiu
  • Pop, Amalia

Abstract

Complex physical systems are considered, involving both random and deterministic phenomena. We introduce a set of age-dependent transition rates accounting for the random jump processes and a set of deterministic equations describing the evolution of the system between two jumps. The age-state probability density obeys a system of integrodifferential balance equations. Assuming the validity of certain separability conditions, a method is presented for reducing the integration of evolution equations to a discrete random walk problem. For pure jump processes a physical interpretation of the main results is given in terms of the probability density for the waiting time. The approach is applied to heavy ion collisions, to electrodiffusion and to stochastic theory of line shape.

Suggested Citation

  • Vlad, Marcel Ovidiu & Pop, Amalia, 1989. "Discrete random walk representations for continuum stochastic dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 159(2), pages 239-255.
    • Handle: RePEc:eee:phsmap:v:159:y:1989:i:2:p:239-255
    DOI: 10.1016/0378-4371(89)90568-2
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