Summary
Let (X t,P x) be a rotation invariant (RI) strong Markov process onR d{0} having a skew product representation [|X t |,\(\theta _{A_t }\)], where (θ t ) is a time homogeneous, RI strong Markov process onS d−1, |X t|, andθ t are independent underP x andA t is a continuous additive functional of |X t|. We characterize the rotation invariant extensions of (X t,P x) toR 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.
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Vuolle-Apiala, J. Excursion theory for rotation invariant Markov processes. Probab. Th. Rel. Fields 93, 153–158 (1992). https://doi.org/10.1007/BF01195226
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DOI: https://doi.org/10.1007/BF01195226
Mathematics Subject Classification
- 60 J 25