具有fBm输入的伽玛反射过程
On the gamma-reflected processes with fBm input
摘要：
定义一个$γ$反映过程$W_γ(t)=Y_H(t)-γ\inf_{s\in[0,t]}Y_H(s)$，$t\ge0$与输入过程$\{Y_H(t), t\ge 0\}$，它是一个分数布朗运动，具有赫斯特指数$H\in (0,1)$和负线性趋势.在风险理论中，$R_γ(t)=u-W_γ(t), t\ge0$被称为损失结转类型的带税风险过程，而在风险理论中，$W_1$被称为队列长度过程。本文研究了在盈余依赖的时间区间$[0, T_u]$上风险过程$R_γ, γ\in [0,1]$的破产概率和破产时间.
英文摘要：
Define a $γ$-reflected process $W_γ(t)=Y_H(t)-γ\inf_{s\in[0,t]}Y_H(s)$, $t\ge0$ with input process $\{Y_H(t), t\ge 0\}$ which is a fractional Brownian motion with Hurst index $H\in (0,1)$ and a negative linear trend. In risk theory $R_γ(t)=u-W_γ(t), t\ge0$ is referred to as the risk process with tax of a loss-carry-forward type, 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 the risk process $R_γ, γ\in [0,1]$ over a surplus dependent time interval $[0, T_u]$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
