Weak convergence of conditioned sums of independent random vectors.

Author:
Thomas M. Liggett

Journal:
Trans. Amer. Math. Soc. **152** (1970), 195-213

MSC:
Primary 60.30

MathSciNet review:
0268940

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Abstract | References | Similar Articles | Additional Information

Abstract: Conditions are given for the weak convergence of processes of the form to tied-down stable processes, where is constructed from normalized partial sums of independent and identically distributed random vectors which are in the domain of attraction of a multidimensional stable law. The conditioning events are defined in terms of subsets of which converge in an appropriate sense to a set of measure zero. Assumptions which the sets must satisfy include that they can be expressed as disjoint unions of ``asymptotically convex'' sets. The assumptions are seen to hold automatically in the special case in which is taken to be a ``natural'' neighborhood of a smooth compact hypersurface in .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1970-0268940-X

Keywords:
Weak convergence,
random vectors,
stable processes,
conditioned processes

Article copyright:
© Copyright 1970
American Mathematical Society