  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 by a Foster-Lyapunov drift condition approach. The test functions
used are naturally related to the geometry of the cone of positive
semi-definite matrices and the drift condition is shown to be satisfied if the
drift term of the defining stochastic differential equation is sufficiently
`negative'. We show easily applicable sufficient conditions for the needed
irreducibility and aperiodicity of the volatility process living in the cone of
positive semidefinite matrices, if the driving L\'evy process is a compound
Poisson process.
