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

Krzysztof Dębicki, and Grzegorz Sikora. "Finite time asymptotics of fluid and ruin models: multiplexed fractional Brownian motions case." Applicationes Mathematicae 38.1 (2011): 107-116. <http://eudml.org/doc/279964>.

@article{KrzysztofDębicki2011,
abstract = {Motivated by applications in queueing fluid models and ruin theory, we analyze the asymptotics of $ℙ(sup_\{t∈[0,T]\} (∑_\{i=1\}^\{n\} λ_i B_\{H_i\}(t) - ct) > u)$, where $\{B_\{H_i\}(t): t ≥ 0\}$, i = 1,...,n, are independent fractional Brownian motions with Hurst parameters $H_i ∈ (0,1]$ and λ₁,...,λₙ > 0. The asymptotics takes one of three different qualitative forms, depending on the value of $min_\{i=1,...,n\}H_i$.},
author = {Krzysztof Dębicki, Grzegorz Sikora},
journal = {Applicationes Mathematicae},
keywords = {exact asymptotics; fractional Brownian motion; Gaussian process; supremum},
language = {eng},
number = {1},
pages = {107-116},
title = {Finite time asymptotics of fluid and ruin models: multiplexed fractional Brownian motions case},
url = {http://eudml.org/doc/279964},
volume = {38},
year = {2011},
}

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
VL - 38
IS - 1
SP - 107
EP - 116
AB - Motivated by applications in queueing fluid models and ruin theory, we analyze the asymptotics of $ℙ(sup_{t∈[0,T]} (∑_{i=1}^{n} λ_i B_{H_i}(t) - ct) > u)$, where ${B_{H_i}(t): t ≥ 0}$, i = 1,...,n, are independent fractional Brownian motions with Hurst parameters $H_i ∈ (0,1]$ and λ₁,...,λₙ > 0. The asymptotics takes one of three different qualitative forms, depending on the value of $min_{i=1,...,n}H_i$.
LA - eng
KW - exact asymptotics; fractional Brownian motion; Gaussian process; supremum
UR - http://eudml.org/doc/279964
ER -