Finite time asymptotics of fluid and ruin models: multiplexed fractional Brownian motions case

Krzysztof Dębicki; Grzegorz Sikora

Applicationes Mathematicae, Tome 38 (2011), p. 107-116 / Harvested from The Polish Digital Mathematics Library

Résumé

Motivated by applications in queueing fluid models and ruin theory, we analyze the asymptotics of $ℙ (s u p_{t \in [0, T]} (\sum_{i = 1}^{n} λ_{i} B_{H_{i}} (t) - c t) > u)$ , where $B_{H_{i}} (t) : t \geq 0$ , i = 1,...,n, are independent fractional Brownian motions with Hurst parameters $H_{i} \in (0, 1]$ and λ₁,...,λₙ > 0. The asymptotics takes one of three different qualitative forms, depending on the value of $m i n_{i = 1, . . ., n} H_{i}$ .

Publié le : 2011-01-01

Zbl 1216.60031

EUDML-ID : urn:eudml:doc:279964

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     title = {Finite time asymptotics of fluid and ruin models: multiplexed fractional Brownian motions case},
     journal = {Applicationes Mathematicae},
     volume = {38},
     year = {2011},
     pages = {107-116},
     zbl = {1216.60031},
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Krzysztof Dębicki; Grzegorz Sikora. Finite time asymptotics of fluid and ruin models: multiplexed fractional Brownian motions case. Applicationes Mathematicae, Tome 38 (2011) pp. 107-116. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am38-1-8/