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We establish bounds on expected values of various geometric quantities thatdescribe the size of the convex hull spanned by a path of the standard planarBrownian motion. Expected values of the perimeter and the area of the Brownianconvex hull are known explicitly, and satisfactory bounds on the expected valueof its diameter can be found in the literature as well. In this work weinvestigate circumradius and inradius of the Brownian convex hull and obtainlower and upper bounds on their expected values. Our other goal is to findbounds on the related inverse processes (that correspond to the perimeter,area, diameter, circumradius and inradius of the convex hull) which provide uswith some information on the speed of growth of the size of the Brownian convexhull.

Bounds on the size of the convex hull of planar Brownian motion and related inverse processes