EXAMPLE: SupposeXi:i1,2,...are i.i.d.Normal1,1randomvariables, and defineWnexp∑i1nXi. ThenWnhas theLognormaln,ndistribution. It follows that, for anyb0,PWnb1−PWn≤b1−logb−nnn−logb/n→1 asn→becausen−logb/n→. Thus, it makes sense to writeWnp→.52
∙For a certain class ofOp1sequences, taking continuoustransformations is guaranteed to preserve theOp1property. We willcover these sequences in Section 6.∙We have to be careful in general. For example, ifWnX/nwhereX0,WnisOp1(in fact,Wnp→0) but logWnlogX−lognis notOp1.53
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