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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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2017/9140138 |
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| _version_ | 1850218314464231424 |
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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). |
| format | Article |
| id | doaj-art-3aaaa0e23e8f4231a98b85b76a293dff |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| 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 |