Topic
Cramér's theorem
About: Cramér's theorem is a research topic. Over the lifetime, 2 publications have been published within this topic receiving 22 citations.
Papers
TL;DR: In this article, sufficient conditions for convergence of monotone moments of weakly convergent random variables, concerning the rate of convergence, are given, often more convenient than the necessary and sufficient uniform integrability condition.
23 citations
TL;DR: In this paper, it was shown that general metric LDPs are preserved under uniformly continuous mappings, which allows us to transform the result of Borovkov and Mogulskii into standard LDP and give an explicit integral representation of the rate function they found.
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 $R^d$ 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 $R^d$.
3 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 1 |
| 2004 | 1 |