Finite time asymptotics of fluid and ruin models: multiplexed fractional Brownian motions case
Volume 38 / 2011
Applicationes Mathematicae 38 (2011), 107-116
MSC: Primary 60G15; Secondary 60G70, 68M20.
DOI: 10.4064/am38-1-8
Abstract
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 $\min_{i=1,\ldots ,n} H_i$.
