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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.03217 |
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| _version_ | 1866909245025288192 |
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| author | Debicki, Krzysztof Ji, Lanpeng Novikov, Svyatoslav |
| author_facet | Debicki, Krzysztof Ji, Lanpeng Novikov, Svyatoslav |
| contents | For $\{B_H(t)= (B_{H,1}(t), \ldots, B_{H,d}(t))^\top,t\ge0\}$, where $\{B_{H,i}(t),t\ge 0\}, 1\le i\le d$ are mutually independent fractional Brownian motions, we obtain the exact asymptotics of $$ \mathbb P (\exists t\ge 0: A B_{H}(t) - μt >νu), \ \ \ \ u\to\infty, $$ where $A$ is a non-singular $d\times d$ matrix and $μ=(μ_1,\ldots, μ_d)^\top\in R^d$, $ν=(ν_1, \ldots, ν_d)^\top \in R^d$ are such that there exists some $1\le i\le d$ such that $μ_i>0, ν_i>0.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_03217 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Probability of entering an orthant by correlated fractional Brownian motion with drift: Exact asymptotics Debicki, Krzysztof Ji, Lanpeng Novikov, Svyatoslav Probability Mathematical Physics For $\{B_H(t)= (B_{H,1}(t), \ldots, B_{H,d}(t))^\top,t\ge0\}$, where $\{B_{H,i}(t),t\ge 0\}, 1\le i\le d$ are mutually independent fractional Brownian motions, we obtain the exact asymptotics of $$ \mathbb P (\exists t\ge 0: A B_{H}(t) - μt >νu), \ \ \ \ u\to\infty, $$ where $A$ is a non-singular $d\times d$ matrix and $μ=(μ_1,\ldots, μ_d)^\top\in R^d$, $ν=(ν_1, \ldots, ν_d)^\top \in R^d$ are such that there exists some $1\le i\le d$ such that $μ_i>0, ν_i>0.$ |
| title | Probability of entering an orthant by correlated fractional Brownian motion with drift: Exact asymptotics |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2402.03217 |