Let (S, ρ) be an ultrametric space satisfying certain conditions and Sk be the quotient space of S with respect to the partition by balls with a fixed radius φ(k). We prove that, for a Hunt process X on S associated with a Dirichlet form (ε, F), a Hunt process Xk on Sk associated with the averaged Dirichlet form (εk, Fk) is Mosco convergent to X, and under certain additional conditions, Xk converges weakly to X. Moreover, we give a sufficient condition for the Markov property of X to be preserved under the canonical projection πk to Sk. In this case, we see that the projected process πk ◦ X is identical in law to Xk and converges almost surely to X.
|ジャーナル||Publications of the Research Institute for Mathematical Sciences|
|出版ステータス||Published - 2014|
ASJC Scopus subject areas
- 数学 (全般)