{"id":356285,"date":"2017-01-20T13:21:52","date_gmt":"2017-01-20T21:21:52","guid":{"rendered":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/?post_type=msr-research-item&#038;p=356285"},"modified":"2018-10-16T19:58:30","modified_gmt":"2018-10-17T02:58:30","slug":"isolated-zeros-brownian-motion-variable-drift","status":"publish","type":"msr-research-item","link":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/publication\/isolated-zeros-brownian-motion-variable-drift\/","title":{"rendered":"Isolated Zeros For Brownian Motion With Variable Drift"},"content":{"rendered":"<p>It is well known that standard one-dimensional Brownian motion <em>B(t)<\/em> has no isolated zeros almost surely. We show that for any <em>\u03b1<\/em> < 1\/2 there are \u03b1-H\u00f6lder continuous functions<em> f<\/em> for which the process <em>B \u2212f<\/em> has isolated zeros with positive probability. We also prove that for any continuous function<em> f,<\/em> the zero set of<em> B \u2212 f<\/em> has Hausdorff dimension at least 1\/2 with positive probability, and 1\/2 is an upper bound on the Hausdorff dimension if <em>f<\/em> is 1\/2-H\u00f6lder continuous or of bounded variation.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>It is well known that standard one-dimensional Brownian motion B(t) has no isolated zeros almost surely. We show that for any \u03b1 < 1\/2 there are \u03b1-H\u00f6lder continuous functions f for which the process B \u2212f has isolated zeros with positive probability. We also prove that for any continuous function f, the zero set of [&hellip;]\n<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":null,"msr_publishername":"Cornell University 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