Fatou's Lemma for Weakly Converging Probabilities
By Eugene A. Feinberg, P. Kasyanov, N. V. Zadoianchuk. 2012
79 citations recorded by the source corpus.
Fatou's lemma states under appropriate conditions that the integral of the lower limit of a sequence of functions is not greater than the lower limit of the integrals. This note describes similar inequalities when, instead of a single measure, the functions are integrated with respect to different measures that form a weakly convergent sequence.
Subfields: Finance, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/e42f99739e561573d9e3551263d1b4cccc371018
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Quantifying Distributional Model Risk via Optimal Transport (2016, unknown): “Further, as c is a nonnegative lower semicontinuous function, it follows from a version of Fatou’s lemma for weakly converging probabilities (see Theorem 1.1 in Feinberg et al. (2014) and references therein) that δ ≥ limk ∫ cdπnk ≥ ∫ cdπ∗.”
- Optimality Conditions for Inventory Control (2016, background): “[33] and references therein) and uniform Fatou’s lemma introduced in Feinberg et al.”