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Asymptotic properties of the Markovian master equations for multi-stationary systems

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  • Ding, E-Jiang

Abstract

In this paper, asymptotic properties of the markovian master equations for multi-stationary systems are discussed. It is proved that the convergence radii of the generating functions are greater than one in most cases. On this basis, the singular perturbation expansion method is generalized to include the case of multi-stationary systems beyond the bifurcation point. The properties of stationary states of the system in the thermodynamic limit are discussed, and the implications of multiplicity of states in the properties of the generating function are established.

Suggested Citation

  • Ding, E-Jiang, 1983. "Asymptotic properties of the Markovian master equations for multi-stationary systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 119(1), pages 317-326.
    • Handle: RePEc:eee:phsmap:v:119:y:1983:i:1:p:317-326
    DOI: 10.1016/0378-4371(83)90163-2
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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. An, Ing & Chen, Shi & Guo, Han-ying, 1984. "Search for the symmetry of the Fokker-Planck equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 128(3), pages 520-528.
    2. Suzuki, Masuo & Liu, Yong & Tsuno, Takashi, 1986. "Revisit to the scaling theory of transient phenomena — Generalization to correlated noise and singular perturbation expansion up to infinite order," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 138(3), pages 433-455.
    3. Jovanovic, Franck & Schinckus, Christophe, 2017. "Econophysics and Financial Economics: An Emerging Dialogue," OUP Catalogue, Oxford University Press, number 9780190205034.

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