  We establish bounds on expected values of various geometric quantities that
describe the size of the convex hull spanned by a path of the standard planar
Brownian motion. Expected values of the perimeter and the area of the Brownian
convex hull are known explicitly, and satisfactory bounds on the expected value
of its diameter can be found in the literature as well. In this work we
investigate circumradius and inradius of the Brownian convex hull and obtain
lower and upper bounds on their expected values. Our other goal is to find
bounds on the related inverse processes (that correspond to the perimeter,
area, diameter, circumradius and inradius of the convex hull) which provide us
with some information on the speed of growth of the size of the Brownian convex
hull.
