Limit theorems for p-variations of solutions of SDEs driven by additive non-Gaussian stable Levy noise
In this paper we study the asymptotic properties of the power variations of stochastic processes of the type X=Y+L, where L is an alpha-stable Levy process, and Y a perturbation which satisfies some mild Lipschitz continuity assumptions. We establish local functional limit theorems for the power var...
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2008
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| Online Access: | https://dx.doi.org/10.48550/arxiv.0811.3769 https://arxiv.org/abs/0811.3769 |
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ftdatacite:10.48550/arxiv.0811.3769 2023-05-15T16:28:35+02:00 Limit theorems for p-variations of solutions of SDEs driven by additive non-Gaussian stable Levy noise Hein, C. Imkeller, P. Pavlyukevich, I. 2008 https://dx.doi.org/10.48550/arxiv.0811.3769 https://arxiv.org/abs/0811.3769 unknown arXiv arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ Probability math.PR FOS Mathematics 60G52; 60F17; 60H10; 62F10; 62M10; 86A40 Preprint Article article CreativeWork 2008 ftdatacite https://doi.org/10.48550/arxiv.0811.3769 2022-04-01T15:07:32Z In this paper we study the asymptotic properties of the power variations of stochastic processes of the type X=Y+L, where L is an alpha-stable Levy process, and Y a perturbation which satisfies some mild Lipschitz continuity assumptions. We establish local functional limit theorems for the power variation processes of X. In case X is a solution of a stochastic differential equation driven by L, these limit theorems provide estimators of the stability index alpha. They are applicable for instance to model fitting problems for paleo-climatic temperature time series taken from the Greenland ice core. : 16 pages, 3 figures Report Greenland Greenland ice core ice core DataCite Metadata Store (German National Library of Science and Technology) Greenland Levy ENVELOPE(-66.567,-66.567,-66.320,-66.320) |
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Open Polar |
| collection |
DataCite Metadata Store (German National Library of Science and Technology) |
| op_collection_id |
ftdatacite |
| language |
unknown |
| topic |
Probability math.PR FOS Mathematics 60G52; 60F17; 60H10; 62F10; 62M10; 86A40 |
| spellingShingle |
Probability math.PR FOS Mathematics 60G52; 60F17; 60H10; 62F10; 62M10; 86A40 Hein, C. Imkeller, P. Pavlyukevich, I. Limit theorems for p-variations of solutions of SDEs driven by additive non-Gaussian stable Levy noise |
| topic_facet |
Probability math.PR FOS Mathematics 60G52; 60F17; 60H10; 62F10; 62M10; 86A40 |
| description |
In this paper we study the asymptotic properties of the power variations of stochastic processes of the type X=Y+L, where L is an alpha-stable Levy process, and Y a perturbation which satisfies some mild Lipschitz continuity assumptions. We establish local functional limit theorems for the power variation processes of X. In case X is a solution of a stochastic differential equation driven by L, these limit theorems provide estimators of the stability index alpha. They are applicable for instance to model fitting problems for paleo-climatic temperature time series taken from the Greenland ice core. : 16 pages, 3 figures |
| format |
Report |
| author |
Hein, C. Imkeller, P. Pavlyukevich, I. |
| author_facet |
Hein, C. Imkeller, P. Pavlyukevich, I. |
| author_sort |
Hein, C. |
| title |
Limit theorems for p-variations of solutions of SDEs driven by additive non-Gaussian stable Levy noise |
| title_short |
Limit theorems for p-variations of solutions of SDEs driven by additive non-Gaussian stable Levy noise |
| title_full |
Limit theorems for p-variations of solutions of SDEs driven by additive non-Gaussian stable Levy noise |
| title_fullStr |
Limit theorems for p-variations of solutions of SDEs driven by additive non-Gaussian stable Levy noise |
| title_full_unstemmed |
Limit theorems for p-variations of solutions of SDEs driven by additive non-Gaussian stable Levy noise |
| title_sort |
limit theorems for p-variations of solutions of sdes driven by additive non-gaussian stable levy noise |
| publisher |
arXiv |
| publishDate |
2008 |
| url |
https://dx.doi.org/10.48550/arxiv.0811.3769 https://arxiv.org/abs/0811.3769 |
| long_lat |
ENVELOPE(-66.567,-66.567,-66.320,-66.320) |
| geographic |
Greenland Levy |
| geographic_facet |
Greenland Levy |
| genre |
Greenland Greenland ice core ice core |
| genre_facet |
Greenland Greenland ice core ice core |
| op_rights |
arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
| op_doi |
https://doi.org/10.48550/arxiv.0811.3769 |
| _version_ |
1766018250156539904 |