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- W2298192007 abstract "Let ${X_i(t),tge0}, 1le ile n$ be independent copies of a random process ${X(t), tge0}$. For a given positive constant $u$, define the set of $r$th conjunctions $C_r(u):={tin[0,1]: X_{r:n}(t)>u}$ with $ X_{r:n}$ the $r$th largest order statistics of $X_i, 1le ile n$. In numerical applications such as brain mapping and digital communication systems, of interest is the approximation of $p_r(u)=mathbb P{C_r(u)neqphi}$. Instead of stationary processes dealt with by Dc{e}bicki et al. (2014), we consider in this paper $X$ a self-similar $mathbb R$-valued process with $P$-continuous sample paths. By imposing the Albin's conditions directly on $X$, we establish an exact asymptotic expansion of $p_r(u)$ as $u$ tends to infinity. As a by-product we derive the asymptotic tail behaviour of the mean sojourn time of $X_{r:n}$ over an increasing threshold. Finally, our findings are illustrated for the case that $X$ is a bi-fractional Brownian motion, a sub-fractional Brownian motion, and a generalized self-similar skew-Gaussian process." @default.
- W2298192007 created "2016-06-24" @default.
- W2298192007 creator A5074437201 @default.
- W2298192007 date "2014-12-12" @default.
- W2298192007 modified "2023-09-26" @default.
- W2298192007 title "Extremes of order statistics of self-similar processes" @default.
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- W2298192007 doi "https://doi.org/10.48550/arxiv.1412.3934" @default.
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