It is shown that under a certain condition on a semimartingale and a time-change, any stochastic integral driven by the time-changed semimartingale is a time-changed stochastic integral driven by the original semimartingale. As a direct consequence, a specialized form of the Itô formula is derived. When a standard Brownian motion is the original semimartingale, classical Itô stochastic differen...

Abstract A form of time series path integral expansion is provided that enables both analytic and numerical temporal effect calculations for a range stochastic processes. All methods rely on finding suitable reproducing kernel associated with an underlying representative algebra to perform the expansion. Birth–death processes can be analysed these techniques, using either standard Doi-Peliti co...