{"paper":{"title":"On certain integral functionals of squared Bessel processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Umut \\c{C}etin","submitted_at":"2012-09-21T20:58:20Z","abstract_excerpt":"Let $X$ be a squared Bessel process. Following a Feynman-Kac approach, the Laplace transforms of joint laws of $(U, \\int_0^{R_y}X_s^p\\,ds)$ are studied where $R_y$ is the first hitting time of $y$ by $X$ and $U$ is a random variable measurable with respect to the history of $X$ until $R_y$. A subset of these results are then used to solve the associated small ball problems for $\\int_0^{R_y}X_s^p\\,ds$ and determine a Chung's law of iterated logarithm. $(\\int_0^{R_y}X_s^p\\,ds)$ is also considered as a purely discontinuous increasing Markov process and its infinitesimal generator is found. The fi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.4919","kind":"arxiv","version":4},"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"}