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Solutions of a class of nonlinear master equations

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  • Feng, S.
  • Zheng, X.

Abstract

Nonlinear master equations in the case of one kind of particle are discussed from the point of view of solving a martingale problem. We get some conditions from which the existence, uniqueness and ergodicity of solutions follow. These results are then used to discuss the phenomenon of phase transitions of the second Schlögl model.

Suggested Citation

  • Feng, S. & Zheng, X., 1992. "Solutions of a class of nonlinear master equations," Stochastic Processes and their Applications, Elsevier, vol. 43(1), pages 65-84, November.
    • Handle: RePEc:eee:spapps:v:43:y:1992:i:1:p:65-84
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    Citations

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    Cited by:

    1. Salah Eddine Choutri & Tembine Hamidou, 2018. "A Stochastic Maximum Principle for Markov Chains of Mean-Field Type," Games, MDPI, vol. 9(4), pages 1-21, October.
    2. Feng, Shui, 1995. "Nonlinear master equation of multitype particle systems," Stochastic Processes and their Applications, Elsevier, vol. 57(2), pages 247-271, June.
    3. Grosskinsky, Stefan & Jatuviriyapornchai, Watthanan, 2019. "Derivation of mean-field equations for stochastic particle systems," Stochastic Processes and their Applications, Elsevier, vol. 129(4), pages 1455-1475.
    4. Chen, Xiong & Feng, Shui, 1996. "Critical phenomenon of a two component nonlinear stochastic system," Statistics & Probability Letters, Elsevier, vol. 30(2), pages 147-155, October.
    5. Xi, Fubao & Zhu, Chao, 2018. "On the martingale problem and Feller and strong Feller properties for weakly coupled Lévy type operators," Stochastic Processes and their Applications, Elsevier, vol. 128(12), pages 4277-4308.

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