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The exact discrete model of a system of linear stochastic differential equations driven by fractional noise
Author(s) -
Simos Theodore
Publication year - 2008
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.2008.00593.x
Subject(s) - mathematics , stochastic differential equation , discrete time and continuous time , noise (video) , gaussian , gaussian noise , discrete time stochastic process , interval (graph theory) , differential equation , state vector , stochastic partial differential equation , mathematical analysis , statistics , continuous time stochastic process , algorithm , computer science , physics , quantum mechanics , combinatorics , artificial intelligence , classical mechanics , image (mathematics)
. This paper derives the exact discrete model (EDM) of a k th‐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.