Vector Stochastic Processes with Pólya‐Type Correlation Structure

This paper introduces a simple method to construct a stationary process on the real line with a Pólya‐type covariance function and with any infinitely divisible marginal distribution, by randomising the timescale of the increment of a second‐order Lévy process with an appropriate positive random variable. With the construction method extended to the multivariate case, we construct vector stochastic processes with Pólya‐type direct covariance functions and with any specified infinitely divisible marginal distributions. This makes available a new class of non‐Gaussian vector stochastic processes with flexible correlation structure for use in modelling and simulation.