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...
| Main Authors: | , , |
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| Format: | Report |
| Language: | unknown |
| Published: |
arXiv
2008
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| Subjects: | |
| Online Access: | https://dx.doi.org/10.48550/arxiv.0811.3769 https://arxiv.org/abs/0811.3769 |
| Summary: | 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 |
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