  The paper introduces a non-linear version of the process convolution
formalism for building covariance functions for multi-output Gaussian
processes. The non-linearity is introduced via Volterra series, one series per
each output. We provide closed-form expressions for the mean function and the
covariance function of the approximated Gaussian process at the output of the
Volterra series. The mean function and covariance function for the joint
Gaussian process are derived using formulae for the product moments of Gaussian
variables. We compare the performance of the non-linear model against the
classical process convolution approach in one synthetic dataset and two real
datasets.
