Two-parameter Bessel processes

We prove the existence of a two-parameter symmetric Markov process associated with the Bessel process in R+ of dimension d⩾2. This process is constructed as a one-parameter process in the space C=C(R+,R+) which is viewed as the path space of the Bessel process. The method consists in introducing a Dirichlet form on C and to prove the existence of an associated process. Thanks to previous papers, analytic and probabilistic potential theories can be developed related to this two-parameter process.