{"paper":{"title":"Persistence exponent for random processes in Brownian scenery","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Fabienne Castell (I2M), Frederique Watbled (LMBA), Nadine Guillotin-Plantard (ICJ)","submitted_at":"2014-07-01T19:17:22Z","abstract_excerpt":"In this paper we consider the persistence properties of random processes in Brownian scenery, which are examples of non-Markovian and\nnon-Gaussian processes. More precisely we study the asymptotic behaviour for large $T$, of the probability $P[ \\sup\\_{t\\in[0,T]} \\Delta\\_t \\leq 1] $\nwhere $\\Delta\\_t = \\int\\_{\\mathbb{R}} L\\_t(x) \\, dW(x).$\nHere $W={W(x); x\\in\\mathbb{R}}$ is a two-sided standard real Brownian motion and ${L\\_t(x); x\\in\\mathbb{R},t\\geq 0}$ is\nthe local time of some self-similar random process $Y$, independent from the process $W$. We thus generalize the results of \\cite{BFFN} wher"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.0364","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"}