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Asymptotic variance of the self-intersections of stable random walks using Darboux-Wiener theory

Abstract:
We present a Darboux-Wiener type lemma as a powerful alternative to the classical Tauberian theorem when monotonicity is not known a priori. We apply it to obtain the exact asymptotics of the variance of the self-intersections of a one-dimensional stable random walk. Finally we prove a functional central limit theorem for stable random walk in random scenery conjectured in [1]. © 2011 Pleiades Publishing, Ltd.

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Publisher copy:
10.1134/S0037446611040082
Journal:
Siberian Mathematical Journal More from this journal
Volume:
52
Issue:
4
Pages:
639-650
Publication date:
2011-07-01
DOI:
ISSN:
0037-4466
Language:
English
Keywords:
Pubs id:
pubs:353222
UUID:
uuid:65eba3ea-0f8e-416e-b701-53358fa60072
Local pid:
pubs:353222
Source identifiers:
353222
Deposit date:
2013-11-16

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