Markov additive friendships
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909347030761472 |
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| author | Döring, Leif Trottner, Lukas Watson, Alexander R. |
| author_facet | Döring, Leif Trottner, Lukas Watson, Alexander R. |
| contents | The Wiener--Hopf factorisation of a Lévy or Markov additive process describes the way that it attains new maxima and minima in terms of a pair of so-called ladder height processes. Vigon's theory of friendship for Lévy processes addresses the inverse problem: when does a process exist which has certain prescribed ladder height processes? We give a complete answer to this problem for Markov additive processes, provide simpler sufficient conditions for constructing processes using friendship, and address in part the question of the uniqueness of the Wiener--Hopf factorisation for Markov additive processes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_09432 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Markov additive friendships Döring, Leif Trottner, Lukas Watson, Alexander R. Probability 60G51, 60J25, 47A68 The Wiener--Hopf factorisation of a Lévy or Markov additive process describes the way that it attains new maxima and minima in terms of a pair of so-called ladder height processes. Vigon's theory of friendship for Lévy processes addresses the inverse problem: when does a process exist which has certain prescribed ladder height processes? We give a complete answer to this problem for Markov additive processes, provide simpler sufficient conditions for constructing processes using friendship, and address in part the question of the uniqueness of the Wiener--Hopf factorisation for Markov additive processes. |
| title | Markov additive friendships |
| topic | Probability 60G51, 60J25, 47A68 |
| url | https://arxiv.org/abs/2308.09432 |