Science China Mathematics

, Volume 61, Issue 4, pp 659–676 | Cite as

Variational formula for the stability of regime-switching diffusion processes

  • Jinghai Shao
  • Lingdi Wang


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.


stability in probability regime-switching diffusions state-dependent M-matrix 


60J27 93E15 60A10 


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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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© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Center for Applied MathematicsTianjin UniversityTianjinChina
  2. 2.School of Mathematics and StatisticsHenan UniversityKaifengChina

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