Geodesic
Bounds for the Extremal Index of Stochastic Recurrent Sequences
Matematičeskie zametki, Tome 98 (2015) no. 3, pp. 349-355.

Voir la notice de l'article provenant de la source Math-Net.Ru

The paper is devoted to the study of the extremal index for some stochastic recurrent sequences and to the derivation of bounds for the cases in which it is impossible to express the extremal index in explicit form.
Keywords: stochastic recurrent sequence, extremal index of a stochastic sequence, marginal distribution, tail index of a stochastic sequence, Jensen's inequality.
Mots-clés : lognormal distribution 
@article{MZM_2015_98_3_a2,
     author = {A. A. Goldaeva},
     title = {Bounds for the {Extremal} {Index} of {Stochastic} {Recurrent} {Sequences}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {349--355},
     publisher = {mathdoc},
     volume = {98},
     number = {3},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2015_98_3_a2/}
}
TY  - JOUR
AU  - A. A. Goldaeva
TI  - Bounds for the Extremal Index of Stochastic Recurrent Sequences
JO  - Matematičeskie zametki
PY  - 2015
SP  - 349
EP  - 355
VL  - 98
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2015_98_3_a2/
LA  - ru
ID  - MZM_2015_98_3_a2
ER  - 
%0 Journal Article
%A A. A. Goldaeva
%T Bounds for the Extremal Index of Stochastic Recurrent Sequences
%J Matematičeskie zametki
%D 2015
%P 349-355
%V 98
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2015_98_3_a2/
%G ru
%F MZM_2015_98_3_a2
A. A. Goldaeva. Bounds for the Extremal Index of Stochastic Recurrent Sequences. Matematičeskie zametki, Tome 98 (2015) no. 3, pp. 349-355. http://geodesic.mathdoc.fr/item/MZM_2015_98_3_a2/

[1] M. Lidbetter, G. Lindgren, Kh. Rotsen, Ekstremumy sluchainykh posledovatelnostei i protsessov, Mir, M., 1989 | MR | Zbl

[2] W. Vervaat, “On a stochastic difference equation and a representation of non-negative infinitely divisible random variables”, Adv. in Appl. Probab., 11:4 (1979), 750–783 | DOI | MR | Zbl

[3] L. de Haan, S. I. Resnick, H. Rootzén, C. G. de Vries, “Extremal behaviour of solutions to a stochastic difference equation with applications to ARCH processes”, Stochastic Process. Appl., 32 (1989), 213–224 | DOI | MR | Zbl

[4] A. A. Goldaeva, “Ispolzovanie protsessov s nepreryvnym vremenem v issledovanii stokhasticheskikh rekurrentnykh posledovatelnostei”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 2010, no. 6, 13–18 | MR | Zbl

[5] O. S. Novitskaya, E. B. Yatsalo, “Ekstremalnoe povedenie rekurrentnykh sluchainykh posledovatelnostei”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 2008, no. 5, 6–10 | MR | Zbl

[6] A. N. Shiryaev, Osnovy stokhasticheskoi finansovoi matematiki, T. 1, 2, Fazis, M., 1998

[7] A. A. Goldaeva, “Ravnomernaya otsenka ekstremalnogo indeksa stokhasticheskikh rekurrentnykh posledovatelnostei”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 2012, no. 2, 51–55 | MR | Zbl