Novikov's condition (original) (raw)

In probability theory, Novikov's condition is the sufficient condition for a stochastic process which takes the form of the Radon–Nikodym derivative in Girsanov's theorem to be a martingale. If satisfied together with other conditions, Girsanov's theorem may be applied to a Brownian motion stochastic process to change from the original measure to the new measure defined by the Radon–Nikodym derivative. Assume that is a real valued adapted process on the probability space and is an adapted Brownian motion: If the condition is fulfilled then the process