{"paper":{"title":"On the gamma-reflected processes with fBm input","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Enkelejd Hashorva, Lanpeng Ji, Peng Liu","submitted_at":"2014-02-11T20:21:09Z","abstract_excerpt":"Define a $\\gamma$-reflected process $W_\\gamma(t)=Y_H(t)-\\gamma\\inf_{s\\in[0,t]}Y_H(s)$, $t\\ge0$ 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 $R_\\gamma(t)=u-W_\\gamma(t), t\\ge0$ 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 $R_\\gamma, \\gamma \\in [0,1]$ over a surplus dependent time interval $[0, T_u]$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.2628","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}