An invariance principle under the total variation distance
نویسندگان
چکیده
منابع مشابه
An invariance principle under the total variation distance
Abstract: Let X1,X2, . . . be a sequence of i.i.d. random variables, with mean zero and variance one. Let Wn = (X1 + . . . +Xn)/ √ n. An old and celebrated result of Prohorov [16] asserts that Wn converges in total variation to the standard Gaussian distribution if and only if Wn0 has an absolutely continuous component for some n0. In the present paper, we give yet another proof and extend Proh...
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ژورنال
عنوان ژورنال: Stochastic Processes and their Applications
سال: 2015
ISSN: 0304-4149
DOI: 10.1016/j.spa.2014.12.010