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MiS Preprint

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

Tobias Fritz


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.

MSC Codes:
06F25, 16Y60, 60F10, 12J15, 14P10
ordered semiring, abstract Positivstellensatz, large deviations

Related publications

2021 Repository Open Access
Tobias Fritz

A generalization of Strassen's Positivstellensatz

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