Abstract:Given the increments of a simple symmetric random walk (Xn) n≥0 , we characterize all possible ways of recycling these increments into a simple symmetric random walk (Yn) n≥0 adapted to the filtration of (Xn) n≥0 . We study the long term behavior of a suitably normalized two-dimensional process ((Xn, Yn)) n≥0 . In particular, we provide necessary and sufficient conditions for the process to converge to a two-dimensional Brownian motion (possibly degenerate). We also discuss cases in which the limit is not Gaus… Show more
Set email alert for when this publication receives citations?
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.