Electronic Resource
Springer
Probability theory and related fields
5 (1966), S. 175-179
ISSN:
1432-2064
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary If random variables X n converge in distribution to a nondegenerate random variable X, and if transformations a n X n +b n of them, with a n 〉0, also converge in distribution to X, then a n →1 and b n →0. Moreover, the group of transformations x→ax+b that preserve the distribution of a nondegenerate random variable consists either of the identity alone, or of the identity together with the reflection through some point. For proofs see [4], [5], or [6]. This paper gives the corresponding results for k-dimensional random vectors.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00536653
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