Skip to content
DraconiticResearch
Search Sources API
190,335 studies31 sourcesUpdated 37 min ago
Peer-reviewedCC BY 4.0Mathematics

Cumulative Rewards for Birth–Death Processes with Catastrophes

  • Junping Li1,2
  1. 1School of General Education, Guangdong University of Science & Technology, Dongguan 523083, China
  2. 2School of Mathematics and Statistics, Central South University, Changsha 410083, China
Open at sourceDOICite

Abstract

This paper investigates cumulative reward functionals for birth–death processes with Poisson-driven total catastrophes. Using an auxiliary killed Markov process, we derive the integral equations for the distribution and expectation of the reward accumulated up to the first catastrophe, and establish the existence and uniqueness of bounded solutions. Explicit expressions are provided for constant birth–death rates. The asymptotic limits of the scaled expected reward are analyzed for vanishing and diverging catastrophe rates, with limiting behavior classified by the recurrence of the underlying catastrophe-free birth–death process.

Related

  1. Darboux transformations of linear birth-death processes
    José Arcia-Manoleskos, Manuel Domínguez de la Iglesia
    arXivPreprintarXiv licenceFull textAnalysis & PDEsProbabilityarXiv
  2. Space-time large deviations for continuum birth-and-death processes
    Benedikt Jahnel, Jonas Köppl, Yannic Steenbeck +1
    arXivPreprintCC BY-NC-SA 4.0Full textProbabilityarXiv
  3. The principal spectral gap for birth--death processes with a strong Allee effect
    Dun Zhou
    arXivPreprintarXiv licenceFull textDynamical systemsProbabilityarXiv
  4. Quasi-stationary distributions and sharp metastable asymptotics for birth--death processes with a strong Allee effect
    Tian Hou, Kaige Yan, Dun Zhou
    arXivPreprintarXiv licenceFull textDynamical systemsProbabilityarXiv
  5. Random walk in a null recurrent birth-and-death dynamical environment
    Luiz Renato Fontes, Pablo A. Gomes
    arXivPreprintCC BY 4.0Full textProbabilityarXiv

Cite

BibTeXRIS
BibTeX
@article{li2026cumulative,
  title = {{Cumulative Rewards for Birth–Death Processes with Catastrophes}},
  author = {Junping Li},
  journal = {Mathematics},
  year = {2026},
  month = oct,
  doi = {10.3390/math14213864},
  url = {https://www.mdpi.com/2227-7390/14/21/3864},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Cumulative Rewards for Birth–Death Processes with Catastrophes
AU  - Junping Li
PY  - 2026
DA  - 2026/10/22
JO  - Mathematics
DO  - 10.3390/math14213864
UR  - https://www.mdpi.com/2227-7390/14/21/3864
AB  - This paper investigates cumulative reward functionals for birth–death processes with Poisson-driven total catastrophes. Using an auxiliary killed Markov process, we derive the integral equations for the distribution and expectation of the reward accumulated up to the first catastrophe, and establish the existence and uniqueness of bounded solutions. Explicit expressions are provided for constant birth–death rates. The asymptotic limits of the scaled expected reward are analyzed for vanishing and diverging catastrophe rates, with limiting behavior classified by the recurrence of the underlying catastrophe-free birth–death process.
SN  - 2227-7390
ER  -