EXCURSION THEORY FOR ROTATION INVARIANT MARKOV-PROCESSES

Let (X(t), P(x)) be a rotation invariant (RI) strong Markov process on R(d)\{0} having a skew product representation [\X(t)\, theta(At)], where (theta(t)) is a time homogeneous, RI strong Markov process on S(d-1), \X(t)\ and theta(t) are independent under P(x) and A(t) is a continuous additive functional of \X(t)\. We characterize the rotation invariant extensions of (X(t), P(x)) to R(d). Two examples are given: the diffusion case, where especially the Walsh's Brownian motion (Brownian hedgehog) is considered, and the case where (X(t), P(x)) is self-similar.