A note about an upper bound for a hitting time of the fractional Ornstein-Uhlenbeck process
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929460444397568 |
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| author | B, Wilson Cabanillas |
| author_facet | B, Wilson Cabanillas |
| contents | In this brief note we give an upper bound for $P(τ_u < T)$ with $T>0$, where $τ_u$ is the exit time defined as $τ_u:=\inf \{ t\geq 0 \, : \, X_t\geq u \}$ and $(X_t)_{t\geq 0}$ is the fractional Ornstein-Uhlenbeck processes which satisfies the following stochastic differential equation \begin{equation*} dX_t =-λX_t dt+ εdB_t^H\quad ε>0,\;λ>0 \end{equation*} with $(B_t^H)_{t\geq 0}$ as the fractional brownian motion with parameter of Hurst $H\in ]0,1]$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_08240 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note about an upper bound for a hitting time of the fractional Ornstein-Uhlenbeck process B, Wilson Cabanillas Probability In this brief note we give an upper bound for $P(τ_u < T)$ with $T>0$, where $τ_u$ is the exit time defined as $τ_u:=\inf \{ t\geq 0 \, : \, X_t\geq u \}$ and $(X_t)_{t\geq 0}$ is the fractional Ornstein-Uhlenbeck processes which satisfies the following stochastic differential equation \begin{equation*} dX_t =-λX_t dt+ εdB_t^H\quad ε>0,\;λ>0 \end{equation*} with $(B_t^H)_{t\geq 0}$ as the fractional brownian motion with parameter of Hurst $H\in ]0,1]$. |
| title | A note about an upper bound for a hitting time of the fractional Ornstein-Uhlenbeck process |
| topic | Probability |
| url | https://arxiv.org/abs/2408.08240 |