Random Time Change and Some Applications

Abstract

This thesis is a survey of known results concerning random time change and its applications. It will cover basic probabilistic concepts and then follow with a detailed look at major results in several branches of probability all concerning random time change. The first of these major results is a theorem on how an increasing process adapted to a filtration can be used to transform the time scale and filtration. Next we show how an arbitrary continuous local martingale can be changed into a Brownian motion. We then show that a simple point process can be changed into a Poisson process using a random time change. Lastly, we look at an application of random time change to create solutions of stochastic differential equations.