abstract: We shall give a construction of the Wiener integrals relative to the centered Bessel processes based on the Brascamp-Lieb inequality. Another approach via Hardy's inequality will be discussed. We shall then present a new proof of the Brascamp-Lieb like inequalities and related FKG inequality due to a coupling of SDEs. The first part is a joint work with Y. Hariya, F. Hirsch, M. Yor and the second one with K. Toukairin.