virtuell

We consider a family of multivariate autoregressive stochastic sequences that restart when hit a neighbourhood of the origin, and study the distributional limit of their stationary distributions when the autoregressive coefficient tends to one, the noise scaling parameter tends to zero, and the neighbourhood size varies. We obtain a non-standard limit theorem where the limiting distribution is a mixture of an atomic distribution and an absolutely continuous distribution whose marginals, in turn, are mixtures of distributions of signed absolute values of normal random variables. Several examples are discussed.

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Matthias Schulte

TU Hamburg