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Some Functional Stable Limit Theorems

Published online by Cambridge University Press:  20 November 2018

D. R. Beuerman
D. R. Beuerman*
Affiliation:
Queen's University, Kingston, Ontario
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Let Xl,X2,X3, … be a sequence of independent and identically distributed (i.i.d.) random variables which belong to the domain of attraction of a stable law of index α≠1. That is,

1

where

and

where L(n) is a function of slow variation; also take S0=0, B0=l.

In §2, we are concerned with the weak convergence of the partial sum process to a stable process and the question of centering for stable laws and drift for stable processes.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 16 , Issue 2 , June 1973 , pp. 173 - 177
Copyright
Copyright © Canadian Mathematical Society 1973

References

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