On necessary and sufficient conditions for convergence of probability measures in variation
Let \(\{p^ n\}\) and \(\{\) \(\tilde p{}^ n\}\) be two sequences of probability measures. The convergence of the variation \(\|\tilde p^ n-p^ n\|\) to zero as \(n\to\infty \) is considered. Various types of necessary and sufficient conditions for this convergence in terms of likelihood ratios of their restrictions and in terms of some predictable characteristics are derived.
scientific article; zbMATH DE number 3872363
scientific article