{"paper":{"title":"On the Supremum of gamma-reflected Processes with Fractional Brownian Motion as Input","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Enkelejd Hashorva, Lanpeng Ji, Vladimir I. Piterbarg","submitted_at":"2013-06-09T09:32:03Z","abstract_excerpt":"Let $X_H(t), t\\ge 0$ be a fractional Brownian motion with Hurst index $H\\in(0,1}$ and define a gamma-reflected process $W_\\Ga(t)=X_H(t)-ct-\\gammainf_{s\\in[0,t]}\\left(X_H(s)-cs \\right)$, $t\\ge0$ with $c>0,\\gamma \\in [0,1]$ two given constants. In this paper we establish the exact tail asymptotic behaviour of $\\sup_{t\\in [0,T]} W_\\gamma(t)$ for any $T\\in (0,\\IF]$. Furthermore, we derive the exact tail asymptotic behaviour of the supremum of certain non-homogeneous mean-zero Gaussian random fields."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.2000","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"}