On convergence of types and processes in Euclidean space |
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Authors: | Ishay Weissman |
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Institution: | (1) Faculty of Industrial and Management Engineering, Technion, Haifa, Israel |
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Abstract: | Let be an Euclidean space; Y
n
, Z, U random vectors in ; h
n
, g
n
affine transformations and let þ be a subgroup of the group G of all the in vertible affine transformations, closed relative to G. Suppose that gn
and
where Z is nonsingular. The behaviour of
n
= h
n
g
n
–1
as n![rarr](/content/n014777604q25561/xxlarge8594.gif) is discussed first. The results are used then to prove that if
![exist](/content/n014777604q25561/xxlarge8707.gif) for all t (0, ), where h
n
þ and Z
1 is nonsingular and nonsymmetric with respect to þ then
H,
for all t (0, ) and is a continuous homomorphism of the multiplicative group of (0, ) into þ. The explicit forms of the possible are shown. |
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Keywords: | |
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