  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).
