Geodesic
Finite time asymptotics of fluid and ruin models: multiplexed fractional Brownian motions case
Krzysztof Dębicki1 ; Grzegorz Sikora2
1 Mathematical Institute University of Wrocław Pl. Grunwaldzki 2/4 50-384 Wrocław, Poland
2 Institute of Mathematics and Computer Science Wrocław University of Technology Wybrzeże Wyspiańskiego 27 50-370 Wrocław, Poland
Applicationes Mathematicae, Tome 38 (2011) no. 1, pp. 107-116.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Motivated by applications in queueing fluid models and ruin theory, we analyze the asymptotics of $$ {\Bbb P}\Bigl(\sup_{t\in [0,T]} \Bigl( \sum_{i=1}^n \lambda_iB_{H_i}(t)-ct\Bigr)>u\Bigr), $$ where $\{B_{H_i}(t):t\ge 0\}$, $i=1,\ldots ,n$, are independent fractional Brownian motions with Hurst parameters $H_i\in (0,1]$ and $\lambda_1,\ldots ,\lambda_n>0$. The asymptotics takes one of three different qualitative forms, depending on the value of $\min_{i=1,\ldots ,n} H_i$.
DOI : 10.4064/am38-1-8
Keywords: motivated applications queueing fluid models ruin theory analyze asymptotics bbb bigl sup bigl sum lambda ct bigr bigr where ldots independent fractional brownian motions hurst parameters lambda ldots lambda asymptotics takes three different qualitative forms depending value min ldots

Krzysztof Dębicki 1 ; Grzegorz Sikora 2

1 Mathematical Institute University of Wrocław Pl. Grunwaldzki 2/4 50-384 Wrocław, Poland
2 Institute of Mathematics and Computer Science Wrocław University of Technology Wybrzeże Wyspiańskiego 27 50-370 Wrocław, Poland 
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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) no. 1, pp. 107-116. doi : 10.4064/am38-1-8. http://geodesic.mathdoc.fr/articles/10.4064/am38-1-8/

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