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Variational formula for the stability of regime-switching diffusion processes

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Abstract

The asymptotical stability in probability is studied for diffusion processes and regime-switching diffusion processes in this work. For diffusion processes, some criteria based on the integrability of the functionals of the coeffcients are given, which yield a useful comparison theorem on stability with respect to some nonlinear systems. For regime-switching diffusion processes, some criteria based on the idea of a variational formula are given. Both state-independent and state-dependent regime-switching diffusion processes are investigated in this work. These conditions are easily verified and are shown to be sharp by examples.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 11301030, 11401169 and 11431014), and Key Scientific Research Projects of Henan Province (Grant No. 16A110010).

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Authors and Affiliations

  1. Center for Applied Mathematics, Tianjin University, Tianjin, 300072, China

    Jinghai Shao

  2. School of Mathematics and Statistics, Henan University, Kaifeng, 475001, China

    Lingdi Wang

Authors
  1. Jinghai Shao
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  2. Lingdi Wang
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Correspondence to Lingdi Wang.

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Shao, J., Wang, L. Variational formula for the stability of regime-switching diffusion processes. Sci. China Math. 61, 659–676 (2018). https://doi.org/10.1007/s11425-016-9015-1

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  • DOI: https://doi.org/10.1007/s11425-016-9015-1

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