Representations of isotropic Gaussian random fields with homogeneous increments

Abstract

We present series expansions and moving average representations of isotropic Gaussian random fields with homogeneous increments, making use of concepts of the theory of vibrating strings. We illustrate our results using the example of Lévy's fractional Brownian motion onℝN.

Lectures on Gaussian Processes

“…One can find variants of expansion (12.6) for other Gaussian processes and random fields in [57,58,133]. …”

An Optimal Series Expansion of the Multiparameter Fractional Brownian Motion

“…is weakly relatively compact in the space C(B). To prove this, one can use the same method as in the proof of Theorem 4.1 in [5]. Proof of Theorem 1 is finished.…”

“…u l mn (x)ξ l mn of the expansion (5). The number of terms in this sum is asymptotically equal to the integral (u+1)(u/2+v)≤q,u≥0,v≥1…”