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Note on the stochastic theory of a self-catalytic chemical reaction. I

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  • Dambrine, S.
  • Moreau, M.

Abstract

By using the spectral theory of the master equation, it is shown generally that a self-catalytic chemical system may evolve according to two widely different time scales in this case. The shorter one describes the evolution towards a quasi-stationary state which is the stochastic equivalent of the macroscopic stationary state. The larger time characterizes the final evolution towards total absorption; it is coarsely evaluated for an arbitrary system and more precisely for a non step-by-step reaction. Detailed application to step-by-step reactions is given in a second article.

Suggested Citation

  • Dambrine, S. & Moreau, M., 1981. "Note on the stochastic theory of a self-catalytic chemical reaction. I," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 106(3), pages 559-573.
    • Handle: RePEc:eee:phsmap:v:106:y:1981:i:3:p:559-573
    DOI: 10.1016/0378-4371(81)90126-6
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    References listed on IDEAS

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    1. Malek-Mansour, M. & Brenig, L. & Horsthemke, W., 1977. "A stochastic approach to the kinetic theory of gases," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 88(3), pages 407-424.
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    Cited by:

    1. van Doorn, Erik A. & Pollett, Philip K., 2013. "Quasi-stationary distributions for discrete-state models," European Journal of Operational Research, Elsevier, vol. 230(1), pages 1-14.

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