Extremal behaviour of solutions to a stochastic difference equation with applications to ARCH processes
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Publication:1822829
DOI10.1016/0304-4149(89)90076-8zbMath0679.60029OpenAlexW2035995445MaRDI QIDQ1822829
Holger Rootzén, Casper G. de Vries, Sidney I. Resnick, Laurens De Haan
Publication date: 1989
Published in: Stochastic Processes and their Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/0304-4149(89)90076-8
Central limit and other weak theorems (60F05) Stationary stochastic processes (60G10) Sample path properties (60G17) Stochastic analysis (60H99)
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Cites Work
- Unnamed Item
- Unnamed Item
- Extremes and related properties of random sequences and processes
- Extreme value theory for moving average processes
- Random difference equations and renewal theory for products of random matrices
- Generalized autoregressive conditional heteroscedasticity
- On a stochastic difference equation and a representation of non–negative infinitely divisible random variables
- Modelling the persistence of conditional variances
- Maxima and exceedances of stationary Markov chains
- Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation
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