Guillotin-Plantard, Nadine; Le Ny, Arnaud A functional limit theorem for a 2D-random walk with dependent marginals. (English) Zbl 1189.60066 Electron. Commun. Probab. 13, 337-351 (2008). Summary: We prove a non-standard functional limit theorem for a two dimensional simple random walk on some randomly oriented lattices. This random walk, already known to be transient, has different horizontal and vertical fluctuations leading to different normalizations in the functional limit theorem, with a non-Gaussian horizontal behavior. We also prove that the horizontal and vertical components are not asymptotically independent. Cited in 9 Documents MSC: 60F17 Functional limit theorems; invariance principles 60K37 Processes in random environments Keywords:random walks; random environments; random sceneries; oriented lattices; functional limit theorems; self-similar and non-Gaussian processes PDFBibTeX XMLCite \textit{N. Guillotin-Plantard} and \textit{A. Le Ny}, Electron. Commun. Probab. 13, 337--351 (2008; Zbl 1189.60066) Full Text: DOI arXiv EuDML EMIS