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An almost sure invariance principle for stochastic approximation procedures in linear filtering theory. (English) Zbl 0877.62078

Summary: We consider a class of stochastic approximation procedures that arises in linear filtering and regression theory. Our main result asserts that the stochastic approximation process satisfies an almost sure invariance principle (with a certain rate of convergence) if the partial sums of the errors do.

MSC:

62L20 Stochastic approximation
60F17 Functional limit theorems; invariance principles
62M20 Inference from stochastic processes and prediction
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