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).
W. Hu, "Itô's Formula, the Stochastic Exponential, and Change of Measure on General Time Scales," Abstract and Applied Analysis, vol. 2017, Hindawi Limited, Apr 2017.
The definitive version is available at https://doi.org/10.1155/2017/9140138
Mathematics and Statistics
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© 2017 Wenqing Hu, All rights reserved.
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01 Apr 2017