Title: Geometric Ergodicity of the MUCOGARCH(1,1) process,
Abstract: For the multivariate COGARCH(1,1) volatility process we show sufficient
conditions for the existence of a unique stationary distribution, for the
geometric ergodicity and for the finiteness of moments of the stationary
distribution. One of the conditions demands a sufficiently fast exponential
decay of the MUCOGARCH(1,1) volatility process. Furthermore, we show easily
applicable sufficient conditions for the needed irreducibility of the
volatility process living in the cone of positive semidefinite matrices, if the
driving Lévy process is a compound Poisson process.