On branching models with alarm triggerings

Autor:	Sergey Utev, Philippe Picard, Claude Lefèvre
Rok vydání:	2020
Předmět:	Statistics and Probability education.field_of_study Distribution (number theory) Markov chain General Mathematics Population Birth–death process Branching (linguistics) ALARM Stopping time Applied mathematics State (computer science) Statistics Probability and Uncertainty education Mathematics
Zdroj:	Journal of Applied Probability. 57:734-759
ISSN:	1475-6072 0021-9002
Popis:	We discuss a continuous-time Markov branching model in which each individual can trigger an alarm according to a Poisson process. The model is stopped when a given number of alarms is triggered or when there are no more individuals present. Our goal is to determine the distribution of the state of the population at this stopping time. In addition, the state distribution at any fixed time is also obtained. The model is then modified to take into account the possible influence of death cases. All distributions are derived using probability-generating functions, and the approach followed is based on the construction of families of martingales.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::c1b5309ba2a3a99fe852aa6caa38920c https://doi.org/10.1017/jpr.2020.24 Zobrazit plný text záznamu