A class of models for non-stationary Gaussian processes

Abstract

Non-stationary processes reducible to stationary processes, oscillatory processes, and truncated Karhunen–Loève or Fourier series are currently used to represent non-stationary Gaussian processes and generate samples of these processes. This paper presents alternative models for non-stationary, continuous-time Gaussian processes and develops Monte Carlo simulation algorithms based on these models. Two classes of models and Monte Carlo algorithms are considered depending on whether the target Gaussian process is or is not Markov. Generally, the Monte Carlo simulation algorithms for non-stationary Gaussian–Markov processes are more efficient and simpler to implement than the algorithms for non-stationary Gaussian processes. Examples are presented to illustrate the models for non-stationary Gaussian processes discussed in the paper and the Monte Carlo simulation algorithms based on these models. The examples include non-stationary Gaussian processes that satisfy and violate the Markov property.