{"paper":{"title":"Grey Brownian motion local time: Existence and weak-approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jos\\'e Lu\\'is da Silva, Mohamed Erraoui","submitted_at":"2013-06-17T19:14:26Z","abstract_excerpt":"In this paper we investigate the class of grey Brownian motions $B_{\\alpha,\\beta}$ ($0<\\alpha<2$, $0<\\beta\\leq1$). We show that grey Brownian motion admits different representations in terms of certain known processes, such as fractional Brownian motion, multivariate elliptical distribution or as a subordination. The weak convergence of the increments of $B_{\\alpha,\\beta}$ in $t$, $w$-variables are studied. Using the Berman criterium we show that $B_{\\alpha,\\beta}$ admits a $\\lambda$-square integrable local time $L^{B_{\\alpha,\\beta}}(\\cdot,I)$ almost surely ($\\lambda$ Lebesgue measure). Moreov"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.3956","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"}