Title

Continuous-time models of generalized random walks

Date of Completion

January 2000

Keywords

Mathematics|Physics, Elementary Particles and High Energy

Degree

Ph.D.

Abstract

The Wiener process is the classical example of a mathematical model for Brownian movement. Wiener viewed Brownian movement essentially as a random walk: a Brownian particle's position at time t equals the sum of displacements over successive time intervals that partition [0, t]. This is a guideline to the definition of integrator. We can reverse the point of view and ask the following question: Under which (minimal) conditions is the process retrievable from its increments? ^ We present a construction (a blueprint) that is based on the application of multidimensional measure theory. This construction is extendible to processes indexed by n parameters. ^