Abstract and Applied Analysis

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

Wenqing Hu

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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


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