{"paper":{"title":"Minkowski dimension of Brownian motion with drift","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Perla Sousi, Philippe H. A. Charmoy, Yuval Peres","submitted_at":"2012-08-02T19:56:05Z","abstract_excerpt":"We study fractal properties of the image and the graph of Brownian motion in $\\R^d$ with an arbitrary c{\\`a}dl{\\`a}g drift $f$. We prove that the Minkowski (box) dimension of both the image and the graph of $B+f$ over $A\\subseteq [0,1]$ are a.s.\\ constants. We then show that for all $d\\geq 1$ the Minkowski dimension of $(B+f)(A)$ is at least the maximum of the Minkowski dimension of $f(A)$ and that of $B(A)$. We also prove analogous results for the graph. For linear Brownian motion, if the drift $f$ is continuous and $A=[0,1]$, then the corresponding inequality for the graph is actually an equ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.0586","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"}