Itô's formula, the stochastic exponential and change of measure on general time scales

Abstract: We provide an It^{o}'s formula for stochastic dynamical equation on general time scales. Based on this It^{o}'s formula we give a closed form expression for stochastic exponential on general time scales. We then demonstrate a 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).