This book presents papers that originally appeared in the Japanese journal ""Sugaku"". The papers fall into the general area of mathematical analysis as it pertains to probability and statistics, dynamical systems, differential equations and analytic function theory. Among the topics discussed are: stochastic differential equations, spectra of the Laplacian and Schrodinger operators, nonlinear partial differential equations which generate dissipative dynamical systems, fractal analysis on self-similar sets and their global structure of analytic functions.