Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2017, Article ID 9140138, 13 pages
https://doi.org/10.1155/2017/9140138
Research Article

Itô’s Formula, the Stochastic Exponential, and Change of Measure on General Time Scales

Department of Mathematics and Statistics, Missouri University of Science and Technology (Formerly University of Missouri, Rolla), Rolla, MO, USA

Correspondence should be addressed to Wenqing Hu; ude.tsm@newuh

Received 8 December 2016; Revised 28 March 2017; Accepted 29 March 2017; Published 18 April 2017

Academic Editor: Allan Peterson

Copyright © 2017 Wenqing Hu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We provide an Itô formula for stochastic dynamical equation on general time scales. Based on this Itô’s formula we give a closed-form expression for stochastic exponential on general time scales. We then demonstrate Girsanov’s change of measure formula in the case of general time scales. Our result is being applied to a Brownian motion on the quantum time scale (-time scale).