Skorokhod $M_{1}$ convergence of maxima of multivariate linear processes with heavy-tailed innovations and random coefficients
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866909264175431680 |
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| author | Krizmanic, Danijel |
| author_facet | Krizmanic, Danijel |
| contents | We derive functional convergence of the partial maxima stochastic processes of multivariate linear processes with weakly dependent heavy-tailed innovations and random coefficients. The convergence takes place in the space of $\mathbb{R}^{d}$--valued càdlàg functions on $[0,1]$ endowed with the weak Skorokhod $M_{1}$ topology. We also show that this topology in general can not be replaced by the standard (or strong) $M_{1}$ topology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_04054 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Skorokhod $M_{1}$ convergence of maxima of multivariate linear processes with heavy-tailed innovations and random coefficients Krizmanic, Danijel Probability We derive functional convergence of the partial maxima stochastic processes of multivariate linear processes with weakly dependent heavy-tailed innovations and random coefficients. The convergence takes place in the space of $\mathbb{R}^{d}$--valued càdlàg functions on $[0,1]$ endowed with the weak Skorokhod $M_{1}$ topology. We also show that this topology in general can not be replaced by the standard (or strong) $M_{1}$ topology. |
| title | Skorokhod $M_{1}$ convergence of maxima of multivariate linear processes with heavy-tailed innovations and random coefficients |
| topic | Probability |
| url | https://arxiv.org/abs/2208.04054 |