Sojourns of locally self-similar Gaussian processes
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arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866914667064983552 |
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| author | Novikov, Svyatoslav M. |
| author_facet | Novikov, Svyatoslav M. |
| contents | Given a Gaussian risk process $R(t)=u+c(t)-X(t),t\ge 0$, the cumulative Parisian ruin probability on a finite time interval $[0,T]$ with respect to $L \geq 0$ is defined as the probability that the sojourn time that the risk process $R$ spends under the level 0 on this time interval $[0,T]$ exceeds $L$. In this contribution we derive exact asymptotic approximations of the cumulative Parisian ruin probability for a general class of Gaussian processes introduced in [9] assuming that $X$ is locally self-similar. We illustrate our findings with several examples. As a byproduct we show that Berman's constants can be defined alternatively by a self-similar Gaussian process which could be quite different to the fractional Brownian motion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_03267 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sojourns of locally self-similar Gaussian processes Novikov, Svyatoslav M. Probability Primary 60G15, Secondary 60G70 Given a Gaussian risk process $R(t)=u+c(t)-X(t),t\ge 0$, the cumulative Parisian ruin probability on a finite time interval $[0,T]$ with respect to $L \geq 0$ is defined as the probability that the sojourn time that the risk process $R$ spends under the level 0 on this time interval $[0,T]$ exceeds $L$. In this contribution we derive exact asymptotic approximations of the cumulative Parisian ruin probability for a general class of Gaussian processes introduced in [9] assuming that $X$ is locally self-similar. We illustrate our findings with several examples. As a byproduct we show that Berman's constants can be defined alternatively by a self-similar Gaussian process which could be quite different to the fractional Brownian motion. |
| title | Sojourns of locally self-similar Gaussian processes |
| topic | Probability Primary 60G15, Secondary 60G70 |
| url | https://arxiv.org/abs/2402.03267 |