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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
86/2018

A generalization of Strassen's Positivstellensatz and its application to large deviation theory

Tobias Fritz

Abstract

Strassen's Positivstellensatz is a powerful but little known result for preordered semirings satisfying a boundedness condition, and characterizes the relaxed preorder induced by all monotone homomorphisms to $\mathbb{R}_+$ in terms of a condition involving large powers. Here, we generalize and strengthen Strassen's theorem: as a generalization, we replace the boundedness condition by a polynomial growth condition; as a strengthening, we prove two further equivalent characterizations of the homomorphism preorder in our generalized setting.

We then present two applications to large deviation theory, giving results on the asymptotic comparison of one random walk relative to another. This gives a probabilistic interpretation for one moment-generating function to dominate another, in the context of bounded random variables.

Received:
Oct 4, 2018
Published:
Oct 16, 2018
MSC Codes:
06F25, 16Y60, 60F10, 12J15, 14P10
Keywords:
ordered semiring, abstract Positivstellensatz, large deviations

Related publications

inJournal
2021 Repository Open Access
Tobias Fritz

A generalization of Strassen's Positivstellensatz

In: Communications in algebra, 49 (2021) 2, pp. 482-499