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Let X = fX(t);t 2RNg be a Gaussian random fleld in Rd with stationary increments. For any Borel set E ‰ RN, we provide su-cient conditions for the image X(E) to be a Salem set or to have interior points by studying the asymptotic properties of the Fourier transform of the occupation measure of X and the continuity of the local times of X on E, respectively. Our results extend and improve the previous theorems of Pitt (24) and Kahane (12, 13) for fractional Brownian motion.

Images of Gaussian random fields: Salem sets and interior points