Non-standard limits for a family of autoregressive stochastic sequences

We examine the influence of using a restart mechanism on stationary distributions particular class Markov chains. Namely, we consider family multivariate autoregressive stochastic sequences that when hit neighbourhood origin, and study their distributional limits coefficient tends to one, noise scaling parameter zero, size varies. show may change significantly limiting distribution. obtain limit theorem with novel type distribution, mixture an atomic distribution absolutely continuous whose marginals, in turn, are mixtures signed absolute values normal random variables. In particular, provide conditions for be normal, like case without mechanism. The main is accompanied by number examples auxiliary results own interest.