Corpus ID: 235458668

Sturm-Liouville Theory and Decay Parameter for Quadratic Markov Branching Processes

@inproceedings{Chen2020SturmLiouvilleTA,
  title={Sturm-Liouville Theory and Decay Parameter for Quadratic Markov Branching Processes},
  author={Anyue Chen and Yong Chen and W. Gao and Xiaohan Wu},
  year={2020}
}
For a quadratic Markov branching process (QMBP), we show that the decay parameter is equal to the first eigenvalue of a Sturm-Liouville operator associated with the PDE that the generating function of the transition probability satisfies. The proof is based on the spectral properties of the Sturm-Liouville operator. Both the upper and lower bounds of the decay parameter are given explicitly by means of a version of Hardy inequality. Two examples are provided to illustrate our results. The… Expand

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