Gaussian Markov Processes

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C. E. Rasmussen & C. K. I. Williams, Gaussian Processes for Machine Learning, the MIT Press, 2006,ISBN 2006 Massachusetts Institute of BGaussian Markov ProcessesParticularly when the index set for a stochastic process is one-dimensional suchas the real line or its discretization onto the integer lattice, it is very interestingto investigate the properties of GaussianMarkovprocesses (GMPs). In thisAppendix we useX(t) to define a stochastic process with continuous time pa-rametert. In the discrete time case the process is ,X 1,X0,X1,...etc. We assume that the process has zero mean and is, unless otherwise stated, discrete-time autoregressive (AR) process of orderpcan be written asAR processXt=p k=1akXt k+b0Zt,( )whereZt N(0,1) and allZt s are.

C. E. Rasmussen & C. K. I. Williams, Gaussian Processes for Machine Learning, the MIT Press, 2006, ISBN 026218253X. 2006 Massachusetts Institute of Technology.c www.GaussianProcess.org/gpml

  Processes, Markov, Markov processes