Random Circles and Fields on Circles.

Abstract

Abstract : The aim is to describe the exact shapes of objects that were meant to be circles or cylinders. The shapes are modeled as random fields whose parameter spaces are the intended shapes. A specific random fields on a true circle is introduced via exponential smoothing of a random noise, on the circle, with stationary and independent increments. The result is a stationary stochastically continuous random field. When the noise is the white noise, the result is the unique continuous stationary Gaussian random field on the circle. A similar definition for cylinders yields infinite dimensional Ornstein Uhlenbeck processes.