Exit times for multivariate autoregressive processes

We study exit times from a set for a family of multivariate autoregressive processes with normallydistributed noise. By using the large deviation principle, and other methods, we show that the asymptoticbehavior of the exit time depends only on the set itself and on the covariance matrix of the stationarydistribution of the process. The results are extended to exit times from intervals for the univariateautoregressive process of order n, where the exit time is of the same order of magnitude as the exponentialof the inverse of the variance of the stationary distribution.