Finite time asymptotics of fluid and ruin models:
multiplexed fractional Brownian motions case
Applicationes Mathematicae, Tome 38 (2011) no. 1, pp. 107-116
Cet article a éte moissonné depuis 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 $\min_{i=1,\ldots ,n} H_i$.
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
Affiliations des auteurs :
Krzysztof Dębicki 1 ; Grzegorz Sikora 2
@article{10_4064_am38_1_8,
author = {Krzysztof D\k{e}bicki and Grzegorz Sikora},
title = {Finite time asymptotics of fluid and ruin models:
multiplexed fractional {Brownian} motions case},
journal = {Applicationes Mathematicae},
pages = {107--116},
year = {2011},
volume = {38},
number = {1},
doi = {10.4064/am38-1-8},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/am38-1-8/}
}
TY - JOUR AU - Krzysztof Dębicki AU - Grzegorz Sikora TI - Finite time asymptotics of fluid and ruin models: multiplexed fractional Brownian motions case JO - Applicationes Mathematicae PY - 2011 SP - 107 EP - 116 VL - 38 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.4064/am38-1-8/ DO - 10.4064/am38-1-8 LA - en ID - 10_4064_am38_1_8 ER -
%0 Journal Article %A Krzysztof Dębicki %A Grzegorz Sikora %T Finite time asymptotics of fluid and ruin models: multiplexed fractional Brownian motions case %J Applicationes Mathematicae %D 2011 %P 107-116 %V 38 %N 1 %U http://geodesic.mathdoc.fr/articles/10.4064/am38-1-8/ %R 10.4064/am38-1-8 %G en %F 10_4064_am38_1_8
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
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