{"paper":{"title":"A Weak Approximation for the Extrema's Distributions of L\\'evy Processes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Amir T. Payandeh Najafabadi, Dan Z. Kucerovsky","submitted_at":"2017-01-19T15:14:49Z","abstract_excerpt":"Suppose $X_{t}$ is a one-dimensional and real-valued L\\'evy process started from $X_0=0$, which ({\\bf 1}) its nonnegative jumps measure $\\nu$ satisfying $\\int_{\\Bbb R}\\min\\{1,x^2\\}\\nu(dx)<\\infty$ and ({\\bf 2}) its stopping time $\\tau(q)$ is \\emph{either} a geometric \\emph{or} an exponential distribution with parameter $q$ independent of $X_t$ and $\\tau(0)=\\infty.$ This article employs the Wiener-Hopf Factorization (WHF) to find, an $L^{p^*}({\\Bbb R})$ (where $1/{p^*}+1/p=1$ and $1<p\\leq2$), approximation for the extrema's distributions of $X_{t}.$ Approximating the finite (infinite)-time ruin "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.05466","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"}