arXiv subjects
Publications and source records attributed to Brita Jung.
By using the large deviation principle, we investigate the expected exit time from the interval [-1,1] of a process of autoregressive type. The case when the autoregression function f is linear and the innovations have a normal distribution has been treated before. In this paper, we extend the results to more general functions f, with the main focus on piecewise linear functions.
In this paper, a branching process model of the Northern Spotted Owl is simulated. We focus on the time until extinction. It is shown how an approximation of the model with a multivariate autoregressive process works well near the equilibrium, but does not give a good estimate of the time until extinction. We also show that introduction of randomness in some of the parameters previously assumed to be constants shortens the time until extinction considerably.
We study exit times from a set for a family of multivariate autoregressive processes with normally distributed noise. By using the large deviation principle, and other methods, we show that the asymptotic behavior of the exit time depends only on the set itself and on the covariance matrix of the stationary distribution of the process. The results are extended to exit times from intervals for the univariate autoregressive process of order n, where the exit time is of the same order of magnitude as the exponential of the inverse of the variance of the stationary distribution.