Abstract
For a one-dimensional random walk in random scenery (RWRS) on Z, we determine its quenched weak limits by applying Strassen's functional law of iterated logarithm. As a consequence, conditioned on the random scenery, the one dimensional RWRS does not converge in law, in contrast with the multi-dimensional case.
Highlights
Random walks in random sceneries were introduced independently by Kesten and Spitzer [9]and by Borodin [3, 4]
In [8], the case of the planar random walk was studied, the authors proved a quenched version of the annealed central limit theorem obtained by Bolthausen in [2]
We prove that under these assumptions, there is no quenched distributional limit theorem for K
Summary
Random walks in random sceneries were introduced independently by Kesten and Spitzer [9]and by Borodin [3, 4]. In [8], the case of the planar random walk was studied, the authors proved a quenched version of the annealed central limit theorem obtained by Bolthausen in [2]. | ξ), the limit points of the law of Kn, as n → ∞, under the topology of weak convergence of measures, are equal to the set of the laws of random variables in ΘB, with
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
