Stability of overshoots of Markov additive processes
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2021
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866914811950923776 |
|---|---|
| author | Döring, Leif Trottner, Lukas |
| author_facet | Döring, Leif Trottner, Lukas |
| contents | We prove precise stability results for overshoots of Markov additive processes (MAPs) with finite modulating space. Our approach is based on the Markovian nature of overshoots of MAPs whose mixing and ergodic properties are investigated in terms of the characteristics of the MAP. On our way we extend fluctuation theory of MAPs, contributing among others to the understanding of the Wiener-Hopf factorization for MAPs by generalizing Vigon's équations amicales inversés known for Lévy processes. Using the Lamperti transformation the results can be applied to self-similar Markov processes. Among many possible applications, we study the mixing behavior of stable processes sampled at first hitting times as a concrete example. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2102_03238 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Stability of overshoots of Markov additive processes Döring, Leif Trottner, Lukas Probability 60J25, 37A25, 62M05 We prove precise stability results for overshoots of Markov additive processes (MAPs) with finite modulating space. Our approach is based on the Markovian nature of overshoots of MAPs whose mixing and ergodic properties are investigated in terms of the characteristics of the MAP. On our way we extend fluctuation theory of MAPs, contributing among others to the understanding of the Wiener-Hopf factorization for MAPs by generalizing Vigon's équations amicales inversés known for Lévy processes. Using the Lamperti transformation the results can be applied to self-similar Markov processes. Among many possible applications, we study the mixing behavior of stable processes sampled at first hitting times as a concrete example. |
| title | Stability of overshoots of Markov additive processes |
| topic | Probability 60J25, 37A25, 62M05 |
| url | https://arxiv.org/abs/2102.03238 |