Maximal inequalities for bessel processes

Abstract

and the boundary point 0 is a trap if 0 , a reflecting boundary if 0 < < 2 , and an entrance boundary if 2 . (For more information about Bessel processes we shall refer the reader to [4], [5], [7], [8], [9], [11], [13] and [14].) The Bessel processes of dimension 1 are submartingales. The Bessel processes of dimension 0 are supermartingales. However, the Bessel processes of dimension 0 < < 1 are not semimartingales. The Bessel process Z of dimension = n 2 N may be realized as the radial part of the n-dimensional Brownian motion B(n) = B1(t); . . . ; Bn(t) t 0 :