Markov tail chains

Preprint, Research, Other literature type English OPEN
Janssen, A.; Segers, J.;
  • Publisher: Applied Probability Trust
  • Journal: issn: 0021-9002
  • Publisher copyright policies & self-archiving
  • Subject: tail chain | tail-switching potential | 60H25 | 60J05 | 62P05 | 60G70, 60J05 (primary) 60G10, 60H25, 62P05 (secondary) | multivariate regular variation | extreme value distribution | random walk | autoregressive conditional heteroskedasticity | 60G70 | stochastic difference equation | Mathematics - Probability | (multivariate) Markov chain | 60G10

The extremes of a univariate Markov chain with regularly varying stationary marginal distribution and asymptotically linear behavior are known to exhibit a multiplicative random walk structure called the tail chain. In this paper we extend this fact to Markov c... View more
  • References (34)
    34 references, page 1 of 4

    Basrak, B., Davis, R. A. and Mikosch, T. (2002). A characterization of multivariate regular variation. Ann. Appl. Probab. 12, 908-920.

    Basrak, B., Davis, R. A. and Mikosch, T. (2002). Regular variation of GARCH processes. Stoch. Proc. Appl. 99, 95-115.

    Basrak, B. and Segers, J. (2009). Regularly varying multivariate time series. Stoch. Proc. Appl. 119, 1055-1080.

    Billingsley, P. (1968). Convergence of Probability Measures, Wiley, New York.

    Boman, J. and Lindskog, F. (2009). Support theorems for the Radon transform and Cram´er-Wold theorems, J. Theoret. Probab. 22, 683-710.

    Bortot, P. and Coles, S. G. (2000). A sufficiency property arising from the characterization of extremes of Markov chains. Bernoulli 6, 183-190.

    Bortot, P. and Coles, S. G. (2003). Extremes of Markov chains with tail switching potential. J. R. Stat. Soc. Ser. B Stat. Methodol. 65, 851-867.

    Buraczewski, D., Damek, E. and Mirek, M. (2012). Asymptotics of stationary solutions of multivariate stochastic recursions with heavy tailed inputs and related limit theorems. Stoch. Proc. Appl. 122, 42-67.

    Collamore, J. F. and Vidyashankar, A. N. (2013). Tail estimates for stochastic fixed point equations via nonlinear renewal theory. Stoch. Proc. Appl., forthcoming. arXiv:1103.2317

    Coles, S. G., Smith, R. L., and Tawn, J. A. (1997). A seasonal Markov model for extremely low temperatures. Environmetrics 5, 221-239.

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