Central limit theorem and increment conditions

Let [phi] be a convex function defined on R+, with [phi](0) = 0 and limx-->0[phi](x)/x=0. We show that there exists a uniformly bounded process (Xt) on [0,1] with continuous sample paths that satisfies the increment condition for every u < t, E([phi]( Xt- Xu)) [less-than-or-equals, slant] t - u. but that fails the CLT.

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Year of publication:	1986
Authors:	Rhee, WanSoo T.
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 4.1986, 4, p. 191-195
Publisher:	Elsevier
Keywords:	stochastic processes continuous sample path central limit theorem increment conditions

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10005319857