Exit times for some processes with normally distributed noise

This thesis deals with methods to get bounds of the asymptotic behavior of the expected exit time for some processes with normally distributed noise. Mainly, autoregressive processes of different types are treated. Methods using the large deviation principle or comparison with return times give upper bounds. A martingale method and a method for normally distributed random variables give lower bounds. Combination of these methods gives the strongest results, such as the limit of the asymptotic behavior of an exit time for the multivariate autoregressive process.