Equivalence of Gaussian measures for some nonstationary random fields

✍ Scribed by Michael L Stein

• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 263 KB
• Volume: 123
• Category: Article
• ISSN: 0378-3758
• DOI: 10.1016/s0378-3758(03)00144-7

✦ Synopsis

Gaussian random ÿelds whose covariance structures are described by a power law model provide a simple and exible class of models for isotropic random ÿelds. This class includes fractional Brownian ÿelds as a special case. Because these random ÿelds are nonstationary, the extensive results available on equivalence of Gaussian measures for stationary models do not apply to them. This work shows that results on equivalence for two stationary Gaussian random ÿeld models extend in a natural way to the equivalence of a stationary model and a power law model. This result is used to show that if we use a power law model for predicting a random ÿeld at unobserved locations when in fact the random ÿeld is stationary, we can obtain asymptotically optimal predictions as long as the high frequency behavior of the true spectral density is su ciently close to the high frequency behavior of the spectral density of the power law model.