|Publisher DOI:||10.1016/j.spa.2021.09.006||Title:||Non-standard limits for a family of autoregressive stochastic sequences||Language:||English||Authors:||Foss, Sergey
|Keywords:||Autoregressive model; Characteristic function; Limiting distribution; Normal distribution; Restart mechanism; Stationary distribution||Issue Date:||20-Sep-2021||Publisher:||Elsevier||Source:||Stochastic Processes and their Applications 142: 432-461 (2021-12-01)||Abstract (english):||
We examine the influence of using a restart mechanism on the stationary distributions of a particular class of Markov chains. Namely, we consider a family of multivariate autoregressive stochastic sequences that restart when hit a neighbourhood of the origin, and study their distributional limits when the autoregressive coefficient tends to one, the noise scaling parameter tends to zero, and the neighbourhood size varies. We show that the restart mechanism may change significantly the limiting distribution. We obtain a limit theorem with a novel type of limiting distribution, 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. In particular, we provide conditions for the limiting distribution to be normal, like in the case without restart mechanism. The main theorem is accompanied by a number of examples and auxiliary results of their own interest.
|URI:||http://hdl.handle.net/11420/10471||ISSN:||0304-4149||Journal:||Stochastic processes and their applications||Institute:||Mathematik E-10||Document Type:||Article||More Funding information:||The work is supported in part by Mathematical Center in Akademgorodok under agreement No. 075-15-2019-1675 with the Ministry of Science and Higher Education of the Russian Federation.|
|Appears in Collections:||Publications without fulltext|
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