Forward-convex convergence in probability of sequences of nonnegative random variables

DOI10.1090/S0002-9939-2012-11373-5zbMath1268.60032arXiv1002.1889MaRDI QIDQ4907123

Gordan Žitković, Constantinos Kardaras

Publication date: 4 March 2013

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1002.1889

zbMATH Keywords

necessary and sufficient conditionsconvergence in probability

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence (28A20) Probabilistic measure theory (60A10)

Related Items (7)

Convergence in measure under finite additivity ⋮ On local convexity in \(\mathbb{L}^0\) and switching probability measures ⋮ Uniform integrability and local convexity in \(\mathbb L^0\) ⋮ The super-replication theorem under proportional transaction costs revisited ⋮ A simple characterization of tightness for convex solid sets of positive random variables ⋮ No-arbitrage concepts in topological vector lattices ⋮ Dual representation of monotone convex functions on 𝐿⁰

Cites Work

• Separation and duality in locally \(L^0\)-convex modules
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• The asymptotic elasticity of utility functions and optimal investment in incomplete markets
• Convex compactness and its applications
• Numéraire-invariant preferences in financial modeling
• Stochastic integrators
• A generalization of a problem of Steinhaus
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