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

Voir la notice de l'article

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 
@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

Cité par Sources :