A note on ergodic transformations of self-similar Volterra Gaussian processes

Abstract

We derive a class of ergodic transformation of self-similar Gaussian processes that are Volterra, i.e. of type $X_t = \int^t_0 z_X(t,s)dW_s$, $t \in [0,\infty)$, where $z_X$ is a deterministic kernel and $W$ is a standard Brownian motion.