Examples of random fields that can be represented as space-domain scaled stationary Ornstein-Uhlenbeck fields

TL;DR

This paper provides examples of random fields that can be expressed as space-domain scaled stationary Ornstein-Uhlenbeck fields, including Wiener bridges and Kiefer processes, expanding the understanding of their representations.

Contribution

It introduces specific examples of random fields representable as space-domain scaled stationary Ornstein-Uhlenbeck fields, illustrating their applicability.

Findings

Wiener bridges can be represented as scaled Ornstein-Uhlenbeck fields.

Kiefer processes are examples of such representations.

The paper broadens the class of random fields understood through Ornstein-Uhlenbeck models.

Abstract

We give some examples of random fields that can be represented as space-domain scaled stationary Ornstein-Uhlenbeck fields defined on the plane. Namely, we study a tied-down Wiener bridge, tied-down scaled Wiener bridges, a Kiefer process and so called (F,G)-Wiener bridges.