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

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...

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Main Author: Wenqing Hu
Format: Article
Language:English
Published: Wiley 2017-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2017/9140138
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author Wenqing Hu
author_facet Wenqing Hu
author_sort Wenqing Hu
collection DOAJ
description 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).
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spelling doaj-art-3aaaa0e23e8f4231a98b85b76a293dff2025-08-20T02:07:47ZengWileyAbstract and Applied Analysis1085-33751687-04092017-01-01201710.1155/2017/91401389140138Itô’s Formula, the Stochastic Exponential, and Change of Measure on General Time ScalesWenqing Hu0Department of Mathematics and Statistics, Missouri University of Science and Technology (Formerly University of Missouri, Rolla), Rolla, MO, USAWe 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).http://dx.doi.org/10.1155/2017/9140138
spellingShingle Wenqing Hu
Itô’s Formula, the Stochastic Exponential, and Change of Measure on General Time Scales
Abstract and Applied Analysis
title Itô’s Formula, the Stochastic Exponential, and Change of Measure on General Time Scales
title_full Itô’s Formula, the Stochastic Exponential, and Change of Measure on General Time Scales
title_fullStr Itô’s Formula, the Stochastic Exponential, and Change of Measure on General Time Scales
title_full_unstemmed Itô’s Formula, the Stochastic Exponential, and Change of Measure on General Time Scales
title_short Itô’s Formula, the Stochastic Exponential, and Change of Measure on General Time Scales
title_sort ito s formula the stochastic exponential and change of measure on general time scales
url http://dx.doi.org/10.1155/2017/9140138
work_keys_str_mv AT wenqinghu itosformulathestochasticexponentialandchangeofmeasureongeneraltimescales