Recurrence and transience of Gaussian diffusion processes (Q1173896)

The author studies Gaussian diffusions in \(\mathbb{R}^ d\). These diffusions can be described by means of stochastic equations of the form \[ dX^ T_ t=AX_ t dt+B^{1/2}dW_ t, \] where \(A\) and \(B\) are \(d\times d\) matrices, \(B\) positive definite, and \(W_ t\) a standard Brownian motion. The author deals with questions of irreducibility, positive and null recurrence as well as transience. He gives a complete characterization, using the Jordan decomposition of \(A\).