## Abstract and Applied Analysis

- Abstr. Appl. Anal.
- Volume 2017 (2017), Article ID 9140138, 13 pages.

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

#### 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 ($q$-time scale).

#### Article information

**Source**

Abstr. Appl. Anal., Volume 2017 (2017), Article ID 9140138, 13 pages.

**Dates**

Received: 8 December 2016

Revised: 28 March 2017

Accepted: 29 March 2017

First available in Project Euclid: 11 May 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.aaa/1494468087

**Digital Object Identifier**

doi:10.1155/2017/9140138

**Mathematical Reviews number (MathSciNet)**

MR3641849

**Zentralblatt MATH identifier**

06929568

#### Citation

Hu, Wenqing. Itô’s Formula, the Stochastic Exponential, and Change of Measure on General Time Scales. Abstr. Appl. Anal. 2017 (2017), Article ID 9140138, 13 pages. doi:10.1155/2017/9140138. https://projecteuclid.org/euclid.aaa/1494468087