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

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  • Dambrine, S.
  • Moreau, M.

Abstract

The general results of article I on the stochastic representation of the macroscopic stationary state of a self-catalytic chemical system are applied to a step-by-step chemical reaction. The relaxation times to the quasi-stationary state and to the final stationary state are computed by evaluating the first two non-trivial eigenvalues of the transition matrix. The previous results of Oppenheim, Shuler and Weiss are confirmed, precised and extended. The critical and subcritical cases are treated by the same method.

Suggested Citation

  • Dambrine, S. & Moreau, M., 1981. "Note on the stochastic theory of a self-catalytic chemical reaction. II," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 106(3), pages 574-588.
    • Handle: RePEc:eee:phsmap:v:106:y:1981:i:3:p:574-588
    DOI: 10.1016/0378-4371(81)90127-8
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    References listed on IDEAS

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    1. Turner, J.W. & Malek-Mansour, M., 1978. "On the absorbing zero boundary problem in birth and death processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 93(3), pages 517-525.
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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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