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 (-time scale).
Wenqing Hu. "Itô’s Formula, the Stochastic Exponential, and Change of Measure on General Time Scales." Abstr. Appl. Anal. 2017 1 - 13, 2017. https://doi.org/10.1155/2017/9140138