## Abstract and Applied Analysis

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

Wenqing Hu

#### 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
Revised: 28 March 2017
Accepted: 29 March 2017
First available in Project Euclid: 11 May 2017

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

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