Asymptotic variance of the self-intersections of stable random walks using Darboux-Wiener theory
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 ce...
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| Format: | Journal article |
| Language: | English |
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2011
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| _version_ | 1826276332135251968 |
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| author | Deligiannidis, G Utev, SA |
| author_facet | Deligiannidis, G Utev, SA |
| author_sort | Deligiannidis, G |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-06T23:12:21Z |
| format | Journal article |
| id | oxford-uuid:65eba3ea-0f8e-416e-b701-53358fa60072 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T23:12:21Z |
| publishDate | 2011 |
| record_format | dspace |
| spelling | oxford-uuid:65eba3ea-0f8e-416e-b701-53358fa600722022-03-26T18:28:39ZAsymptotic variance of the self-intersections of stable random walks using Darboux-Wiener theoryJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:65eba3ea-0f8e-416e-b701-53358fa60072EnglishSymplectic Elements at Oxford2011Deligiannidis, GUtev, SAWe 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. |
| spellingShingle | Deligiannidis, G Utev, SA Asymptotic variance of the self-intersections of stable random walks using Darboux-Wiener theory |
| title | Asymptotic variance of the self-intersections of stable random walks using Darboux-Wiener theory |
| title_full | Asymptotic variance of the self-intersections of stable random walks using Darboux-Wiener theory |
| title_fullStr | Asymptotic variance of the self-intersections of stable random walks using Darboux-Wiener theory |
| title_full_unstemmed | Asymptotic variance of the self-intersections of stable random walks using Darboux-Wiener theory |
| title_short | Asymptotic variance of the self-intersections of stable random walks using Darboux-Wiener theory |
| title_sort | asymptotic variance of the self intersections of stable random walks using darboux wiener theory |
| work_keys_str_mv | AT deligiannidisg asymptoticvarianceoftheselfintersectionsofstablerandomwalksusingdarbouxwienertheory AT utevsa asymptoticvarianceoftheselfintersectionsofstablerandomwalksusingdarbouxwienertheory |