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Approximation of Invariant Measures for Regime-switching Diffusions

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Abstract

In this paper, we are concerned with long-time behavior of Euler-Maruyama schemes associated with regime-switching diffusion processes. The key contributions of this paper lie in that existence and uniqueness of numerical invariant measures are addressed (i) for regime-switching diffusion processes with finite state spaces by the Perron-Frobenius theorem if the “averaging condition” holds, and, for the case of reversible Markov chain, via the principal eigenvalue approach provided that the principal eigenvalue is positive; (ii) for regime-switching diffusion processes with countable state spaces by means of a finite partition method and an M-Matrix theory. We also reveal that numerical invariant measures converge in the Wasserstein metric to the underlying ones. Several examples are constructed to demonstrate our theory.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Central South University, Changsha, Hunan, 410083, China

    Jianhai Bao

  2. School of Mathematical Science, Beijing Normal University, Beijing, 100875, China

    Jinghai Shao

  3. Department of Mathematics, Swansea University, Singleton Park, SA2 8PP, UK

    Chenggui Yuan

Authors
  1. Jianhai Bao
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  2. Jinghai Shao
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  3. Chenggui Yuan
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Correspondence to Chenggui Yuan.

Additional information

Supported in part by NNSFs of China (Nos. 11301030, 11431014, 11401592) and 985-project.

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Bao, J., Shao, J. & Yuan, C. Approximation of Invariant Measures for Regime-switching Diffusions. Potential Anal 44, 707–727 (2016). https://doi.org/10.1007/s11118-015-9526-x

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