Tohoku Mathematical Journal
2014
September
SECOND SERIES VOL. 66, NO. 3

Tohoku Math. J.
66 (2014), 455-469

Title A CONVERGENCE OF HUNT PROCESSES ON THE RING OF $p$-ADIC INTEGERS AND ITS APPLICATION TO A RANDOM FRACTAL

Author Hiroshi Kaneko and Hisaaki Matusmoto

(Received February 13, 2013, revised August 30, 2013)
Abstract. The convergence of stochastic processes is one of subjects founded on importance of the numerical analysis and physical models with stability. Such practical importance inspires us with vast range of interests as to on which space the convergence can be addressed and which sort of accommodated method is required for demonstrating the convergence on the space in the focus. In this article, we establish an accommodated procedure to show the convergence of Markov processes on the ring of $p$-adic integers which emerges from a construction of random fractals. As seen in other studies on the subject, the notion of generalized Mosco-convergence will be highlighted.

Mathematics Subject Classification. Primary 31C25; Secondary 11F85.
Key words and phrases. Dirichlet spaces, $p$-adic numbers.

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