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Z-theorems limits of stochastic equations.pdf

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http://eprints.org/relation/isVersionOf https://pure.iiasa.ac.at/id/document/70494 http://eprints.org/relation/isVolatileVersionOf https://pure.iiasa.ac.at/id/document/70494 http://eprints.org/relation/isIndexCodesVersionOf https://pure.iiasa.ac.at/id/document/70494 archive 351 disk0/00/00/59/86 2016-01-15 02:11:49 2021-08-27 17:16:58 2016-01-15 02:11:49 article show Anisimov A. Pflug G.C. 1361 0000-0001-8215-3550 pub iis_met prog_rms 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. 2000 published Bernoulli Society for Mathematical Statistics and Probability XJ-00-059 229 public Bernoulli 6 5 917-938 TRUE 1350-7265 FALSE info:eu-repo/semantics/article