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Evolving Systems of Stochastic Differential Equations

Author

Listed:
  • Leonardo Videla

    (Universidad de Valparaíso)

  • Rolando Rebolledo

    (Universidad de Valparaíso)

Abstract

We introduce Evolving Systems of Stochastic Differential Equations. This model generalizes the well-known stochastic differential equations with Markovian switching, enabling the countably many local systems to have solutions in regime-dependent dimension. We provide two constructions, the first one based upon general results on measure-valued processes and the second one partially inspired by recent developments of the theory of concatenation of right processes. We prove the Feller property under very mild assumptions, provide some extensions to the basic model, and show applications of our general framework to a biological model.

Suggested Citation

  • Leonardo Videla & Rolando Rebolledo, 2022. "Evolving Systems of Stochastic Differential Equations," Journal of Theoretical Probability, Springer, vol. 35(3), pages 1662-1705, September.
    • Handle: RePEc:spr:jotpro:v:35:y:2022:i:3:d:10.1007_s10959-021-01098-1
    DOI: 10.1007/s10959-021-01098-1
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    References listed on IDEAS

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    1. Yuan, Chenggui & Mao, Xuerong, 2003. "Asymptotic stability in distribution of stochastic differential equations with Markovian switching," Stochastic Processes and their Applications, Elsevier, vol. 103(2), pages 277-291, February.
    2. Khasminskii, R.Z. & Zhu, C. & Yin, G., 2007. "Stability of regime-switching diffusions," Stochastic Processes and their Applications, Elsevier, vol. 117(8), pages 1037-1051, August.
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