Conditional simulation of multi-variate Gaussian fields via generalization of Hoshiyaʹs technique

This paper generalizes conditional simulation technique of uni-variate Gaussian random fields by the stochastic interpolation proposed by Hoshiya, to multi-variate random fields. The kriging estimation of multi-variate Gaussian fields is proposed, and basic formulation for conditional simulation of multi-variate random fields is established. For the particular case of uncorrelated components of multi-variate field, the formulation reduces to that of uni-variate field given by Hoshiya. The paper also provides proofs of some important properties of the estimation error vector, which guarantee that the conditional simulation of the multi-variate field can be implemented by separately computing its kriging estimate and simulating the error vector. An analytical example of two-variate field is elucidated and some numerical results are discussed.