On the construction of Wiener integrals with respect to certain pseudo-Bessel processes

In previous papers [T. Funaki, Y. Hariya, M. Yor, Wiener integrals for centered powers of Bessel processes, I, Markov Processes Related Fields (2006) (in press); T. Funaki, Y. Hariya, M. Yor, Wiener integrals for centered Bessel and related processes, II, Alea (2006) (in press)], the authors have shown that it is possible to define the Wiener-type integrals , for every and any centered Bessel process with dimension d>1. In this paper, various conditions are stated, showing that such a construction is possible for a large class of processes indexed by two square integrable Brownian functionals. In particular, some of the results previously obtained for the Bessel processes are thus recovered, and in fact shown to extend to certain processes of the form .Bessel processes Ito's representation theorem Wiener integrals Scaling property Gebelein's inequality Hermite and Laguerre series expansions