Generalized cell mapping versus path integration

The paper discusses the relation between the generalized cell mapping(GCM) and the path integration (PI) techniques for estimating the response statistics of white noise drivennonlinear oscillators. Bothmethods are iterative solution techniques for calculating the joint probability density function of the phase space Markov vector processthat solves the st ochastic differential equation associated with the nonlinear dynamic system. It is pointed out that the GCM technique isin fact a special way of implementing the PI method. GCM is byits construction a forward time-stepping procedure, while the general PI method also allows for a combined backward and forward time-stepping solution technique, which is crucial to ward achieving a solution algorithm that can handle phase space dimensions of three and higher.