Work

Cumulative Rewards for Birth–Death Processes with Catastrophes

Year: 2026

Type: article

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.

Source: Mathematics

DOI: 10.3390/math14213864

Author: Junping Li

Institutions: Central South University, Guangdong University of Science and Technology

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funder: National Natural Science Foundation of China