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

Abstract

We provide an Itô's 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 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).

arXiv commentRevised Version accepted by Abstract and Applied Analysis