The exact discrete model of a system of linear stochastic differential equations driven by fractional noise

This paper derives the exact discrete model (EDM) of a kth-order system of stochastic differential equations driven by a vector fractional noise under fixed initial conditions. The EDM can be used for the Gaussian estimation and forecasting with long-memory discrete-time equispaced data. Detailed formulae which are necessary for the construction and numerical evaluation of the Gaussian likelihood under two observation schemes are established. State variables can be observed either at equispaced points in time or as integrals over the observational interval. Copyright 2008 The Author. Journal compilation 2008 Blackwell Publishing Ltd