Z-theorems: Limits of stochastic equations

Anisimov, A. & Pflug, G.C. ORCID: https://orcid.org/0000-0001-8215-3550 (2000). Z-theorems: Limits of stochastic equations. Bernoulli 6 (5) 917-938.

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Let fn(θ,ω) be a sequence of stochastic processes which converge weakly to a limit process f0(θ,ω). We show under some assumptions the weak inclusion of the solution sets θn(ω)={θ:fn(θ,ω)=0} in the limiting solution set θ0(ω)={θ:f0(θ,ω)=0} . If the limiting solutions are almost surely singletons, then weak convergence holds. Results of this type are called Z-theorems (zero-theorems). Moreover, we give various more specific convergence results, which have applications for stochastic equations, statistical estimation and stochastic optimization.

Item Type: Article
Research Programs: Risk, Modeling and Society (RMS)
Depositing User: IIASA Import
Date Deposited: 15 Jan 2016 02:11
Last Modified: 27 Aug 2021 17:16
URI: https://pure.iiasa.ac.at/5986

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