A Note on Uniform Convergence of Stochastic Processes
نویسندگان
چکیده
منابع مشابه
On Convergence of Stochastic Processes
where £iX) is the distribution function of the random variable X,f( ) is a real-valued function 5 continuous almost everywhere (p), and the limit is in the sense of the usual weak convergence of distributions. Equation (2) is usually the real center of interest, for many " limit-distribution theorems" are implicit in it. It is clear that for given {pn} and p, the better theorem of this kind wou...
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en(u, v) = \ (A\x) Vu(x), Vv(x)) #(*) dx, (1.3) jR n) = C?(R ). Here (u,v) denotes the inner product on R. By our assumptions (1.1) and (1.2), it is easy to see that the form (en, 3>(en)) is closable on L\R , <pl dx); we denote the closure of (en5 0(eJ) by (en, 9{en)), where of course 2{en) = 9{t) = H\' \R ). The hypotheses (1.1) and (1.2) ensure that ®(en) = 9{t) = Hl' (R) for all neN. Then (e...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1967
ISSN: 0002-9939
DOI: 10.2307/2035239