 Limit theorems for a branching random walk in a random or varying environmentChunmao Huang and Quansheng Liu Stochastic Processes and their Applications, 2024, vol. 172, issue C Abstract: We consider a branching random walk on the real line with a stationary and ergodic environment (ξn) indexed by time, in which a particle of generation n gives birth to a random number of particles of the next generation, which move on the real line; the joint distribution of the number of children and their displacements on the real line depends on the environment ξn at time n. Let Zn be the counting measure at time n, which counts the number of particles of generation n situated in a Borel set of the real line. For the case where the corresponding branching process is supercritical, we establish limit theorems such as large and moderate deviation principles, central and local limit theorems on the counting measures Zn, convergence of the free energy, law of large numbers on the leftmost and rightmost positions at time n, and the convergence to infinite divisible laws. The varying environment case is also considered. Keywords: Branching random walk; Random environment; Large deviation; Moderate deviation; Central limit theorem; Local limit theorem; Law of large numbers (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:172:y:2024:i:c:s0304414924000462 Ordering information: This journal article can be ordered from DOI: 10.1016/j.spa.2024.104340 Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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