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Exit times for multivariate autoregressive processes

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  • Jung, Brita

Abstract

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.

Suggested Citation

  • Jung, Brita, 2013. "Exit times for multivariate autoregressive processes," Stochastic Processes and their Applications, Elsevier, vol. 123(8), pages 3052-3063.
    • Handle: RePEc:eee:spapps:v:123:y:2013:i:8:p:3052-3063
    DOI: 10.1016/j.spa.2013.03.003
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    Cited by:

    1. Mikael Petersson, 2017. "Quasi-Stationary Asymptotics for Perturbed Semi-Markov Processes in Discrete Time," Methodology and Computing in Applied Probability, Springer, vol. 19(4), pages 1047-1074, December.

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