A convergence of Hunt processes on the ring of $p$-adic integers and its application to a random fractal

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.