This paper studies the following three problems. 1. When does a measure on a self-similar set have the volume doubling property with respect to a given distance

Assume that there is some analytic structure, a differential equation or a stochastic process for example, on a metric space. To describe asymptotic behaviors o

In this paper, time changes of the Brownian motions on generalized Sierpinski carpets including n-dimensional cube [0,1]n are studied. Intuitively time change c

The book covers the latest research in the areas of mathematics that deal the properties of partial differential equations and stochastic processes on spaces in

This volume contains the proceedings from three conferences: the PISRS 2011 International Conference on Analysis, Fractal Geometry, Dynamical Systems and Econom