Contraction principle for trajectories of random walks and Cramer's theorem for kernel-weighted sums
Abstract
In 2013 A.A. Borovkov and A.A. Mogulskii proved a weaker-than-standard "metric" large deviations principle (LDP) for trajectories of random walks in whose increments have the Laplace transform finite in a neighbourhood of zero. We prove that general metric LDPs are preserved under uniformly continuous mappings. This allows us to transform the result of Borovkov and Mogulskii into standard LDPs. We also give an explicit integral representation of the rate function they found. As an application, we extend the classical Cram'er theorem by proving an LPD for kernel-weighted sums of i.i.d. random vectors in .
Keywords
Cite
@article{arxiv.1909.00374,
title = {Contraction principle for trajectories of random walks and Cramer's theorem for kernel-weighted sums},
author = {Vladislav Vysotsky},
journal= {arXiv preprint arXiv:1909.00374},
year = {2021}
}
Comments
This is a version to be published. Proposition 2.1 added. Section 3 had a number of new results added. An error was fixed -- the M_1 topology and the space BV_0[0,1] were replaced throughout by M_1' and BV[0,1], respectively. Minor changes were made throughout