Change of drift in one-dimensional diffusions

Abstract It is generally understood that a given one-dimensional diffusion may be transformed by Cameron–Martin–Girsanov measure change into another with the same volatility but different drift. But to achieve this, we have know change-of-measure local martingale write down true martingale. We provide complete characterisation of when this happens. This enables us discuss absence arbitrage in generalised Heston model including case where Feller condition for process violated.