{"paper":{"title":"Explicit formulas for Laplace transforms of certain functionals of some time inhomogeneous diffusions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Gyula Pap, Matyas Barczy","submitted_at":"2008-10-16T15:23:24Z","abstract_excerpt":"We consider a process $(X_t)_{t\\in[0,T)}$ given by the SDE $dX_t = \\alpha b(t)X_t dt + \\sigma(t) dB_t$, $t\\in[0,T)$, with initial condition $X_0=0$, where $T\\in(0,\\infty]$, $\\alpha\\in R$, $(B_t)_{t\\in[0,T)}$ is a standard Wiener process, $b:[0,T)\\to R\\setminus\\{0\\}$ and $\\sigma:[0,T)\\to(0,\\infty)$ are continuously differentiable functions. Assuming that $b$ and $\\sigma$ satisfy a certain differential equation we derive an explicit formula for the joint Laplace transform of $\\int_0^t\\frac{b(s)^2}{\\sigma(s)^2}(X_s)^2 ds$ and $(X_t)^2$ for all $t\\in[0,T)$. As an application, we study asymptotic b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.2930","kind":"arxiv","version":2},"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"}