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P. Liu et al., « On the gamma-reflected processes with fBm input », Serveur académique Lausannois, ID : 10.1007/s10986-015-9288-6
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Define a gamma-reflected process W (gamma)(t) = Y (H) (t) -aEuro parts per thousand gamma inf (s aaEuro parts per thousand[0. t]) Y (H) (s), t a parts per thousand 1/2 0, gamma a [0, 1], with {Y (H) (t), t a parts per thousand 1/2 0} a fractional Brownian motion with Hurst index H a (0, 1)and negative linear trend. In risk theory, R (gamma) (t)=u-W-gamma(t), t a parts per thousand 1/2 0, is the risk process with tax of a loss-carry-forward type and initial reserve u a parts per thousand 1/2 0 whereas in queueing theory, W (1) is referred to as the queue length process. In this paper, we investigate the ruin probability and the ruin time of R (gamma) over a reserve-dependent time interval.