English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

	   Let  			 		 $B^{H}$ 		be a fractional Brownian motion in  			 		 $\mathbb{R}^{d}$ 		of Hurst index  			 		 $H\in\left(0,1\right)$ 		,  			 		 $f\;:\;\left[0,1\right]\longrightarrow\mathbb{R}^{d}$ 		a Borel function and  			 		 $A\subset\left[0,1\right]$ 		a Borel set. We provide sufficient conditions for the image  			 		 $(B^{H}+f)(A)$ 		to have a positive Lebesgue measure or to have a non-empty interior. This is done through the study of the properties of the density of the occupation measure of  			 		 $(B^{H}+f)$ 		. Precisely, we prove that if the parabolic Hausdorff dimension of the graph of  f  is greater than  Hd , then the density is a square integrable function. If, on the other hand, the Hausdorff dimension of  A  is greater than  Hd , then it even admits a continuous version. This allows us to establish the result already cited.

Images of fractional Brownian motion with deterministic drift: Positive Lebesgue measure and non-empty interior