Skip to main content
Log in

Law of the Iterated Logarithm for Unstable Gaussian Autoregressive Models

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

We investigate the asymptotic properties of one-dimensional Gaussian autoregressive processes of the second order. We prove the law of the iterated logarithm in the case of an unstable autoregressive model.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

REFERENCES

  1. T. L. Lai, “Gaussian processes, moving averages and quick detection problems,” Ann. Probab. 1, No. 5, 825–837 (1973).

    Google Scholar 

  2. V. V. Buldygin and V. A. Koval', Asymptotic Behavior of Solutions of Stochastic Difference Equations [in Russian], Preprint No. 91.24, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1991).

    Google Scholar 

  3. V. Buldygin and S. Solntsev, Asymptotic Behaviour of Linearly Transformed Sums of Random Variables Kluwer, Dordrecht (1997).

    Google Scholar 

  4. V. A. Koval' and R. Schwabe, “A limit theorem for the maximum of dependent Gaussian random elements in a Banach space,” Ukr. Mat. Zh. 49, No. 7, 1005–1008 (1997).

    Google Scholar 

  5. M. Duflo, Random Iterative Models Springer, Berlin (1997).

    Google Scholar 

  6. A. O. Gel'fond, Finite-Difference Calculus [in Russian], Nauka, Moscow (1967).

    Google Scholar 

  7. V. Strassen, “An invariance principle for the law of the iterated logarithm,” Z. Wahrscheinlichkeitstheor. und verw. Geb. 3, No. 3, 211–226 (1964).

    Google Scholar 

  8. V. O. Koval', “On the law of the iterated logarithm for Gaussian sequences and its applications,” Teor. Ver. Mat. Statist. Issue 54, 66–71 (1996).

    Google Scholar 

  9. X. Chen, “On the law of the iterated logarithm for independent Banach space valued random variables,” Ann. Probab. 21, No. 4, 1991–2011 (1993).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Koval', V.A. Law of the Iterated Logarithm for Unstable Gaussian Autoregressive Models. Ukrainian Mathematical Journal 53, 488–492 (2001). https://doi.org/10.1023/A:1012304724204

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1012304724204

Keywords

Navigation