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Ergodicity and stability of hybrid systems with piecewise constant type state-dependent switching

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  • Shao, Jinghai
  • Wang, Lingdi
  • Wu, Qiong

Abstract

To deal with stochastic hybrid systems with general state-dependent switching, we propose an approximation method by a sequence of stochastic hybrid systems with piecewise constant type switching. The convergence rate in the Wasserstein distance is estimated in terms of the difference between transition rate matrices. Our method is based on an elaborate construction of coupling processes in terms of Skorokhod’s representation theorem for jumping processes. Moreover, we establish explicit criteria on the ergodicity and stability for stochastic hybrid systems with piecewise constant type switching. Some examples are given to illustrate the sharpness of these criteria.

Suggested Citation

  • Shao, Jinghai & Wang, Lingdi & Wu, Qiong, 2023. "Ergodicity and stability of hybrid systems with piecewise constant type state-dependent switching," Stochastic Processes and their Applications, Elsevier, vol. 161(C), pages 1-23.
    • Handle: RePEc:eee:spapps:v:161:y:2023:i:c:p:1-23
    DOI: 10.1016/j.spa.2023.03.014
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    References listed on IDEAS

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    1. J. Michael Harrison & Michael I. Taksar, 1983. "Instantaneous Control of Brownian Motion," Mathematics of Operations Research, INFORMS, vol. 8(3), pages 439-453, August.
    2. Luz Rocío Sotomayor & Abel Cadenillas, 2009. "Explicit Solutions Of Consumption‐Investment Problems In Financial Markets With Regime Switching," Mathematical Finance, Wiley Blackwell, vol. 19(2), pages 251-279, April.
    3. Shao, Jinghai, 2015. "Ergodicity of regime-switching diffusions in Wasserstein distances," Stochastic Processes and their Applications, Elsevier, vol. 125(2), pages 739-758.
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