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- W4230735061 abstract "Let $mathbb {X}=(mathbb {X}_t)_{tgeq 0}$ be the subdiffusive process defined, for any $tgeq 0$, by $mathbb {X}_t = X_{ell _t}$ where $X=(X_t)_{tgeq 0}$ is a Lévy process and $ell _t=inf {s>0; mathcal {K}_s>t }$ with $mathcal {K}=(mathcal {K}_t)_{tgeq 0}$ a subordinator independent of $X$. We start by developing a composite Wiener-Hopf factorization to characterize the law of the pair $(mathbb {T}_a^{({b})}, (mathbb {X} - {b})_{mathbb {T}_a^{({b})}})$ where begin{equation*}mathbb {T}_a^{({b})} = inf {t>0; mathbb {X}_t > a+ {b}_t } end{equation*} with $a in mathbb {R}$ and ${b}=({b}_t)_{tgeq 0}$ a (possibly degenerate) subordinator independent of $X$ and $mathcal {K}$. We proceed by providing a detailed analysis of the cases where either $mathbb {X}$ is a self-similar or is spectrally negative. For the later, we show the fact that the process $(mathbb {T}_a^{({b})})_{ageq 0}$ is a subordinator. Our proofs hinge on a variety of techniques including excursion theory, change of measure, asymptotic analysis and on establishing a link between subdiffusive processes and a subclass of semi-regenerative processes. In particular, we show that the variable $mathbb {T}_a^{({b})}$ has the same law as the first passage time of a" @default.
- W4230735061 created "2022-05-11" @default.
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- W4230735061 date "2021-08-13" @default.
- W4230735061 modified "2023-10-10" @default.
- W4230735061 title "First passage times over stochastic boundaries for subdiffusive processes" @default.
- W4230735061 doi "https://doi.org/10.1090/tran/8534" @default.
- W4230735061 hasPublicationYear "2021" @default.
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