A limit theorem for a class of stationary increments Lévy moving average process with multiple singularities
In this paper we present some new limit theorems for power variations of stationary increment Lévy driven moving average processes. Recently, such asymptotic results have been investigated in [Ann. Probab. 45(6B) (2017), 4477–4528, Festschrift for Bernt Øksendal, Stochastics 81(1) (2017), 360–383] u...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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VTeX
2018-08-01
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| Series: | Modern Stochastics: Theory and Applications |
| Subjects: | |
| Online Access: | https://www.vmsta.org/journal/VMSTA/article/122/info |
| _version_ | 1811222183843725312 |
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| author | Mathias Mørck Ljungdahl Mark Podolskij |
| author_facet | Mathias Mørck Ljungdahl Mark Podolskij |
| author_sort | Mathias Mørck Ljungdahl |
| collection | DOAJ |
| description | In this paper we present some new limit theorems for power variations of stationary increment Lévy driven moving average processes. Recently, such asymptotic results have been investigated in [Ann. Probab. 45(6B) (2017), 4477–4528, Festschrift for Bernt Øksendal, Stochastics 81(1) (2017), 360–383] under the assumption that the kernel function potentially exhibits a singular behaviour at 0. The aim of this work is to demonstrate how some of the results change when the kernel function has multiple singularity points. Our paper is also related to the article [Stoch. Process. Appl. 125(2) (2014), 653–677] that studied the same mathematical question for the class of Brownian semi-stationary models. |
| first_indexed | 2024-04-12T08:11:49Z |
| format | Article |
| id | doaj.art-fbc1c1b0e283401a94e72d017d12d119 |
| institution | Directory Open Access Journal |
| issn | 2351-6046 2351-6054 |
| language | English |
| last_indexed | 2024-04-12T08:11:49Z |
| publishDate | 2018-08-01 |
| publisher | VTeX |
| record_format | Article |
| series | Modern Stochastics: Theory and Applications |
| spelling | doaj.art-fbc1c1b0e283401a94e72d017d12d1192022-12-22T03:40:58ZengVTeXModern Stochastics: Theory and Applications2351-60462351-60542018-08-015329731610.15559/18-VMSTA111A limit theorem for a class of stationary increments Lévy moving average process with multiple singularitiesMathias Mørck Ljungdahl0Mark Podolskij1Aarhus UniversityAarhus UniversityIn this paper we present some new limit theorems for power variations of stationary increment Lévy driven moving average processes. Recently, such asymptotic results have been investigated in [Ann. Probab. 45(6B) (2017), 4477–4528, Festschrift for Bernt Øksendal, Stochastics 81(1) (2017), 360–383] under the assumption that the kernel function potentially exhibits a singular behaviour at 0. The aim of this work is to demonstrate how some of the results change when the kernel function has multiple singularity points. Our paper is also related to the article [Stoch. Process. Appl. 125(2) (2014), 653–677] that studied the same mathematical question for the class of Brownian semi-stationary models.https://www.vmsta.org/journal/VMSTA/article/122/infoLévy processeslimit theoremsmoving averagesfractional processesstable convergencehigh frequency data |
| spellingShingle | Mathias Mørck Ljungdahl Mark Podolskij A limit theorem for a class of stationary increments Lévy moving average process with multiple singularities Modern Stochastics: Theory and Applications Lévy processes limit theorems moving averages fractional processes stable convergence high frequency data |
| title | A limit theorem for a class of stationary increments Lévy moving average process with multiple singularities |
| title_full | A limit theorem for a class of stationary increments Lévy moving average process with multiple singularities |
| title_fullStr | A limit theorem for a class of stationary increments Lévy moving average process with multiple singularities |
| title_full_unstemmed | A limit theorem for a class of stationary increments Lévy moving average process with multiple singularities |
| title_short | A limit theorem for a class of stationary increments Lévy moving average process with multiple singularities |
| title_sort | limit theorem for a class of stationary increments levy moving average process with multiple singularities |
| topic | Lévy processes limit theorems moving averages fractional processes stable convergence high frequency data |
| url | https://www.vmsta.org/journal/VMSTA/article/122/info |
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