Wiener Integrals for Centered Powers of Bessel Processes, I

#### T. Funaki, Y. Hariya, M. Yor

2007, v.13, Issue 1, 21-56

ABSTRACT

The stochastic integrals of Wiener's type will be constructed relatively to the centered $\delta$-dimensional Bessel processes ($BES(\delta)$-processes in short) and their variants based on two different approaches. The first approach, which is the subject of the present paper, goes via Hardy's $L^2$ inequality which is effective for general $BES(\delta )$-processes, their powers and $\bes (\delta )$-bridges. A second approach, developed in [T. Funaki, Y. Hariya and M. Yor, Wiener integrals for centered Bessel and related processes, II. ALEA (Latin American Journal of Probability and Mathematical Statistics), 2006, v.1, 225-240] is via the so-called Brascamp - Lieb inequality which works especially well for the $\bes (\delta )$-processes, $BES(\delta )$-bridges with $\delta > 3$ or for the Brownian meander.

Keywords: Wiener integrals,Bessel Processes,Bessel bridges,Hardy's $L^2$ inequality