期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2013
卷号：X
页码：323-358
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：We consider branching random walks in discrete time where at eachtime unit particles first produce offspring and thereafter the produced offspringparticles move independently according to some nearest neighbour random walk.In our model, the branching random walks live on Z and the particles behavedifferently in visited and unvisited sites. Informally, each site on the positive halflinecontains initially a cookie. On the first visit of a site its cookie is removed andparticles at positions with a cookie reproduce and move differently from particleson sites without cookies. Therefore, the movement and the reproduction of theparticles depend on the previous behaviour of the population of particles.We give a classification in recurrence and transience, i.e. whether infinitely manyparticles visit the origin or not
关键词：Recurrence; Transience; Self-Interacting Branching Process
