FINITE TIME ASYMPTOTICS OF FLUID AND RUIN MODELS: MULTIPLEXED FRACTIONAL BROWNIAN

Abstract. Motivated by applications in queueing fluid models and ruin theory, we analyze the asymptotics of P sup t∈[0,T] ( n∑ i=1 λiBHi(t) − ct> u where {BHi(t) : t ≥ 0}, i = 1,..., n, are independent fractional Brownian motions with Hurst parameters Hi ∈ (0, 1] and λ1,..., λn> 0. The asymp-totics takes one of three different qualitative forms, depending on the value of mini=1,...,nHi. 1. Introduction. Let {BHi(t) : t ≥ 0}, i = 1,..., n, be independent fractional Brownian motions with Hurst parameters Hi ∈ (0, 1], i.e. centered Gaussian processes with stationary increments, continuous sample paths a.s.