Full classification of dynamics for one-dimensional continuous-time Markov chains with polynomial transition rates. Xu, C., Hansen, M. C., & Wiuf, C. Advances in Applied Probability, 55(1):321–355, March, 2023.
Full classification of dynamics for one-dimensional continuous-time Markov chains with polynomial transition rates [link]Paper  doi  bibtex   
@Article{Xu:2023:FCD,
  author =       "Chuang Xu and Mads Christian Hansen and Carsten Wiuf",
  title =        "Full classification of dynamics for one-dimensional
                 continuous-time {Markov} chains with polynomial
                 transition rates",
  journal =      j-ADV-APPL-PROB,
  volume =       "55",
  number =       "1",
  pages =        "321--355",
  month =        mar,
  year =         "2023",
  CODEN =        "AAPBBD",
  DOI =          "https://doi.org/10.1017/apr.2022.20",
  ISSN =         "0001-8678 (print), 1475-6064 (electronic)",
  ISSN-L =       "0001-8678",
  bibdate =      "Wed Mar 22 14:49:08 MDT 2023",
  URL =          "https://www.cambridge.org/core/journals/advances-in-applied-probability/article/full-classification-of-dynamics-for-onedimensional-continuoustime-markov-chains-with-polynomial-transition-rates/E94F590AA003981FDED8AA5CD22CDD1A",
  acknowledgement = ack-nhfb,
  fjournal =     "Advances in Applied Probability",
  journal-URL =  "http://www.jstor.org/journals/00018678.html;
                 https://www.cambridge.org/core/journals/advances-in-applied-probability;
                 http://projecteuclid.org/euclid.aap/",
  onlinedate =   "12 September 2022",
}

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