Geodesic
Local invariance principle for independent and identically distributed random variables
Teoriâ veroâtnostej i ee primeneniâ, Tome 51 (2006) no. 2, pp. 333-357

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It is well known that for a sequence of independent and identically distributed random variables, the corresponding normalized step-processes converge weakly to the Wiener process. A stronger convergence, namely the convergence in variation of the functional distributions of these processes, has been established in [Y. A. Davydov, M. A. Lifshits, and N. V. Smorodina, Local Properties of Distributions of Stochastic Functionals, American Mathematical Society, Providence, RI, 1998] under the finiteness of the Fisher information of the random variables. In this paper we prove such convergences without a Fisher information type condition.
Keywords: invariance principles, local limit theorems.
Mots-clés : convergence in total variation 
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     title = {Local invariance principle for independent and identically distributed random variables},
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J.-Ch. Breton; Yu. A. Davydov. Local invariance principle for independent and identically distributed random variables. Teoriâ veroâtnostej i ee primeneniâ, Tome 51 (2006) no. 2, pp. 333-357. http://geodesic.mathdoc.fr/item/TVP_2006_51_2_a4/