Large deviations for solutions to stochastic recurrence equations under Kesten's condition

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Standard

Large deviations for solutions to stochastic recurrence equations under Kesten's condition. / Buraczewski, Dariusz; Damek, Ewa ; Mikosch, Thomas Valentin; Zienkiewicz, J.

I: Annals of Probability, Bind 41, Nr. 4, 2013, s. 2755-2790.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Buraczewski, D, Damek, E, Mikosch, TV & Zienkiewicz, J 2013, 'Large deviations for solutions to stochastic recurrence equations under Kesten's condition', Annals of Probability, bind 41, nr. 4, s. 2755-2790. https://doi.org/10.1214/12-AOP782

APA

Buraczewski, D., Damek, E., Mikosch, T. V., & Zienkiewicz, J. (2013). Large deviations for solutions to stochastic recurrence equations under Kesten's condition. Annals of Probability, 41(4), 2755-2790. https://doi.org/10.1214/12-AOP782

Vancouver

Buraczewski D, Damek E, Mikosch TV, Zienkiewicz J. Large deviations for solutions to stochastic recurrence equations under Kesten's condition. Annals of Probability. 2013;41(4):2755-2790. https://doi.org/10.1214/12-AOP782

Author

Buraczewski, Dariusz ; Damek, Ewa ; Mikosch, Thomas Valentin ; Zienkiewicz, J. / Large deviations for solutions to stochastic recurrence equations under Kesten's condition. I: Annals of Probability. 2013 ; Bind 41, Nr. 4. s. 2755-2790.

Bibtex

@article{5b25e4b6706a46cb908b99f3a6b1d3a4,
title = "Large deviations for solutions to stochastic recurrence equations under Kesten's condition",
abstract = "In this paper we prove large deviations results for partial sums constructed from the solution to a stochastic recurrence equation. We assume Kesten{\textquoteright}s condition [17] under which the solution of the stochastic recurrence equation has a marginal distribution with power law tails, while the noise sequence of the equations can have light tails. The results of the paper are analogs of those obtained by A.V. and S.V. Nagaev [21, 22] in the case of partial sums of iid random variables. In the latter case, the large deviation probabilities of the partial sums are essentially determined by the largest step size of the partial sum. For the solution to a stochastic recurrence equation, the magnitude of the large deviation probabilities is again given by the tail of the maximum summand, but the exact asymptotic tail behavior is also influenced by clusters of extreme values, due to dependencies in the sequence. We apply the large deviation results to study the asymptotic behavior of the ruin probabilities in the model. (1.1)",
author = "Dariusz Buraczewski and Ewa Damek and Mikosch, {Thomas Valentin} and J. Zienkiewicz",
year = "2013",
doi = "10.1214/12-AOP782",
language = "English",
volume = "41",
pages = "2755--2790",
journal = "Annals of Probability",
issn = "0091-1798",
publisher = "Institute of Mathematical Statistics",
number = "4",

}

RIS

TY - JOUR

T1 - Large deviations for solutions to stochastic recurrence equations under Kesten's condition

AU - Buraczewski, Dariusz

AU - Damek, Ewa

AU - Mikosch, Thomas Valentin

AU - Zienkiewicz, J.

PY - 2013

Y1 - 2013

N2 - In this paper we prove large deviations results for partial sums constructed from the solution to a stochastic recurrence equation. We assume Kesten’s condition [17] under which the solution of the stochastic recurrence equation has a marginal distribution with power law tails, while the noise sequence of the equations can have light tails. The results of the paper are analogs of those obtained by A.V. and S.V. Nagaev [21, 22] in the case of partial sums of iid random variables. In the latter case, the large deviation probabilities of the partial sums are essentially determined by the largest step size of the partial sum. For the solution to a stochastic recurrence equation, the magnitude of the large deviation probabilities is again given by the tail of the maximum summand, but the exact asymptotic tail behavior is also influenced by clusters of extreme values, due to dependencies in the sequence. We apply the large deviation results to study the asymptotic behavior of the ruin probabilities in the model. (1.1)

AB - In this paper we prove large deviations results for partial sums constructed from the solution to a stochastic recurrence equation. We assume Kesten’s condition [17] under which the solution of the stochastic recurrence equation has a marginal distribution with power law tails, while the noise sequence of the equations can have light tails. The results of the paper are analogs of those obtained by A.V. and S.V. Nagaev [21, 22] in the case of partial sums of iid random variables. In the latter case, the large deviation probabilities of the partial sums are essentially determined by the largest step size of the partial sum. For the solution to a stochastic recurrence equation, the magnitude of the large deviation probabilities is again given by the tail of the maximum summand, but the exact asymptotic tail behavior is also influenced by clusters of extreme values, due to dependencies in the sequence. We apply the large deviation results to study the asymptotic behavior of the ruin probabilities in the model. (1.1)

U2 - 10.1214/12-AOP782

DO - 10.1214/12-AOP782

M3 - Journal article

VL - 41

SP - 2755

EP - 2790

JO - Annals of Probability

JF - Annals of Probability

SN - 0091-1798

IS - 4

ER -

ID: 94844134