Time Changes of the Brownian Motion. - Kigami, Jun (Memoirs of the American Mathematical Society, 2019)
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 corresponds to alteration to density of the medium where the heat flows. In case of the Brownian motion on [0, 1]^n, density of the medium is homogeneous and represented by the Lebesgue measure. The author's study includes densities which are singular to the homogeneous one. He establishes a rich class of measures called measures having weak exponential decay. This class contains measures which are singular to the homogeneous one such.