Abstract
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 in the limiting solution set . 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.
Citation
Vladimir V. Anisimov. Georg CH. Pflug. "Z-theorems: limits of stochastic equations." Bernoulli 6 (5) 917 - 938, oct 2000.
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