Sample-path large deviations for a class of heavy-tailed Markov additive processes
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2020
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| _version_ | 1866917620425424896 |
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| author | Chen, Bohan Rhee, Chang-Han Zwart, Bert |
| author_facet | Chen, Bohan Rhee, Chang-Han Zwart, Bert |
| contents | For a class of additive processes driven by the affine recursion $X_{n+1} = A_n X_n + B_n$, we develop a sample-path large deviations principle in the $M_1'$ topology on $D [0,1]$. We allow $B_n$ to have both signs and focus on the case where Kesten's condition holds on $A_1$, leading to heavy-tailed distributions. The most likely paths in our large deviations results are step functions with both positive and negative jumps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2010_10751 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Sample-path large deviations for a class of heavy-tailed Markov additive processes Chen, Bohan Rhee, Chang-Han Zwart, Bert Probability For a class of additive processes driven by the affine recursion $X_{n+1} = A_n X_n + B_n$, we develop a sample-path large deviations principle in the $M_1'$ topology on $D [0,1]$. We allow $B_n$ to have both signs and focus on the case where Kesten's condition holds on $A_1$, leading to heavy-tailed distributions. The most likely paths in our large deviations results are step functions with both positive and negative jumps. |
| title | Sample-path large deviations for a class of heavy-tailed Markov additive processes |
| topic | Probability |
| url | https://arxiv.org/abs/2010.10751 |