Convergences and Projection Markov Property of Markov Processes on Ultrametric Spaces
Kohei Suzuki
Kyoto University, Japan
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Abstract
Let be an ultrametric space with certain conditions and be the quotient space of with respect to the partition by balls with a fixed radius . We prove that, for a Hunt process on associated with a Dirichlet form , a Hunt process on associated with the averaged Dirichlet form is Mosco convergent to , and under certain additional conditions, converges weakly to . Moreover, we give a sufficient condition for the Markov property of to be preserved under the canonical projection to . In this case, we see that the projected process is identical in law to and converges almost surely to .
Cite this article
Kohei Suzuki, Convergences and Projection Markov Property of Markov Processes on Ultrametric Spaces. Publ. Res. Inst. Math. Sci. 50 (2014), no. 3, pp. 569–588
DOI 10.4171/PRIMS/144