Functional limit theorems are generalizations of classical central limit theorems. They allow us not only to approximate the distributions of sums of random variables, but also describe their temporal evolution. The necessary mathematical concepts as well as some sufficient conditions for convergence to a random walk are discussed.
Central limit theorems Convergence Functional limit theorems General limit theorems Gordin’s th Invariance principle Likelihood Lindeberg condition Martingale differences Random walk Separability Skorohod metric
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