Simulation of infinitely divisible random fields

TL;DR

This paper introduces two new methods for approximating and simulating infinitely divisible random fields by approximating their kernel functions, providing error bounds and practical simulation techniques.

Contribution

It presents novel approximation methods based on spectral kernel approximation for infinitely divisible random fields, with derived error bounds and simulation applications.

Findings

Methods effectively approximate the kernel functions

Error bounds are established for the approximations

Simulations demonstrate practical applicability

Abstract

Two methods to approximate infinitely divisible random fields are presented. The methods are based on approximating the kernel function in the spectral representation of such fields, leading to numerical integration of the respective integrals. Error bounds for the approximation error are derived and the approximations are used to simulate certain classes of infinitely divisible random fields.