#
Technical Reports

**Notice: After publication these reports
were not replaced by the final versions of the paper; deviations from
the printed version are possible. **

**
1993
**

Klueppelberg, C. and Mikosch, T. (1993)
Spectral estimates and stable processes. Stoch. Proc. Appl. 47, 323-344.
See here.
**
1998
**

Mikosch, T. and Starica, C. (1998) Limit theory for the sample autocorrelations
and extremes of a GARCH(1,1) process. A shorter version of this paper
appeared in Annals of Statistics. See here.
**
1999
**

The lecture notes Regular Variation, Subexponentiality and Their
Applications in Probability Theory, made
for the heavy-tailed queuing workshop in Eindhoven (1999), can be
found here.
Basrak, B., Davis, R.A. and Mikosch, T. (1999)
The sample acf of a simple bilinear process.
Stoch. Proc. Appl. 83, 1-14.
See here.
**
2002
**

Basrak, B., Davis, R.A. and Mikosch, T. (2002)
Regular variation of GARCH processes.
Stoch. Proc. Appl. 99, 95-116.
See
here.
Basrak, B., Davis, R.A. and Mikosch, T. (2002)
A characterization of multivariate regular variation.
Ann. Appl. Probab. 12, 908-920.
See
here.
Braverman, M., Mikosch, T. and Samorodnitsky, G. (2002) Tail probabilities of subadditive functionals of Levy processes.
Ann. Appl. Probab. 12, 69-100.
See here.
**
2004
**

Embrechts, P. and Mikosch, T. (2004) Mathematical Models in Finance. Encyclopedia of Life Support Systems (www.eolss.com). See here.
Mikosch, T. and Starica, C. (2004)
Stock market risk-return inference. An unconditional non-parametric
approach.
See here.
**
2005
**

Konstantinides, D. and Mikosch, T. (2004)
Large deviations and ruin probabilities for solutions to
stochastic recurrence equations with heavy-tailed innovations.
Annals of Probability 33, 1992-2035.
See here.
Hult, H., Lindskog, F., Mikosch, T. and Samorodnitsky, G. (2005)
Functional large deviations for multivariate regularly varying
random walks. Ann. Appl. Probab. 15, 2651-2680.
See here.
Mikosch, T. (2005)
How to model multivariate extremes if one must? Stat. Neerlandica 59, 324-338.
See here.
**
2006
**

Straumann, D. and Mikosch, T. (2006) Quasi-MLE in heteroscedastic
times series: a stochastic recurrence equations approach.
Annals of Statistics 34, 2449-2495.
See here.
Mikosch, T. and Straumann, D. (2006)
Stable limits of martingale transforms with application
to the estimation of Garch parameters. Annals of
Statistics Volume 34, 493-522.
See here.
Mikosch, T. and Resnick, S. (2006)
Activity rates with very heavy tails.
Stochastic Processes and their Applications 116, 131-155.
See here.
Fay, G., Gonzalez-Arevalo, B., Mikosch, T., Samorodnitsky, G. (2006)
Modeling teletraffic arrivals by a Poisson cluster process.
QESTA 54, 121-140.
See here.
Mikosch, T. (2006)
Copulas: Tales and facts. Extremes 9, pages 3-20,
and
for a rejoinder, pages 55-62.
See here
and
here
Jessen, A.H., Mikosch, T. (2006)
Regularly varying functions.
Publications de l'Institut Mathematique, Nouvelle Serie, 80(94), 171-192.
See here.
**
2007
**

Mikosch, T., Samorodnitsky, G. (2007)
Scaling limits for cumulative inpot process. Mathematics
of OR 32, 890-919.
See here.
**
2008
**

Davis, R.A., Mikosch, T. (2008)
Extreme value theory for space-time processes with heavy-tailed
distributions. Stochastic Processes and their Applications
118, 560-584.
See here.
Cohen, S., Mikosch, T. (2008)
Tail behavior of random products and stochastic exponentials.
Stochastic Processes and their Applications, 118, 333-345.
See here.
**
2009
**

Jacobsen, M., Mikosch, T., Rosinski, J. Samorodnitsky, G. (2009)
Inverse problems for
regular variation of linear filters, a
cancellation property for sigma-finite measures, and
identification of stable laws. Annals of Appied Probability 19,
210-242.
See here.
Davis, R.A. and Mikosch, T. (2009)
The extremogram: A correllogram for extreme events.
Bernoulli 15, 977-1009.
See here.
**
2010
**

Mikosch, T. and Rackauskas, A. (2010)
The limit distribution of the maximum increment of a heavy-tailed random walk.
Bernoulli 16, 1016-1038.
See here.
Can, S.U., Mikosch, T. and Samorodnitsky, G. (2010)
Weak
convergence of the function-indexed
integrated periodogram for infinite variance processes. Bernoulli 16,
995-1015.
See here.
Matsui, M. and Mikosch, T. (2010)
Prediction in a Poisson
cluster model. J. Appl. Probab. 47, 350-366.
See here.
**
2011
**

Jessen, A.H., Mikosch, T. and Samorodnitsky, G. (2011)
Prediction of outstanding payments in a Poisson cluster model.
Scand. Act. J., 214-237.
See here.
Mikosch, T., Pawlas, Z. and Samorodnitsky, G. (2011)
A large deviation principle for Minkowski sums of heavy-tailed random compact
convex sets with finite expectation.
J. Appl. Probab. Special Volume 48A (New Frontiers in Applied Probability. A Festschrift for Soeren Asmussen (Eds. P. Glynn, T. Mikosch and T. Rolski),
133-146.
See here.
Mikosch, T., Pawlas, Z. and Samorodnitsky, G. (2011)
Large deviations for Minkowski sums of heavy-tailed
generally non-convex random compact
sets.
Vestnik St. Petersburg University, Ser. 1, issue 2. Special Issue in Honor of Valentin V. Petrov, pp. 70-78.
See here.
Bartkiewicz, K., Jakubowski, A., Mikosch, T. and Wintenberger, O. (2011)
Stable limits for sums of dependent infinite variance
random variables. Probab. Th. Rel. Fields 150, 337-372.
See here.
**
2012
**

Cribben, I., Davis, R.A. and Mikosch, T. (2012)
Towards estimating extremal serial dependence via the
bootstrapped extremogram.
J. Econometrics 170, 142-152.
See here.
An extended version exists in ArXiv.
**
2013
**

Mikosch, T. and Moser, M. (2013)
The limit distribution of the maximum increment of a random walk
with dependent regularly varying jump sizes.
Probab. Th. Rel. Fields, 156, 249-272
See here.
Mikosch, T. and Rezapour, M. (2013)
Stochastic volatility models with possible extremal clustering.
Bernoulli 19, 1688-1713.
See here.
Buraczewski, D., Damek, E., Mikosch, T. and Zienkiewicz, J. (2013)
Large deviations for solutions to stochastic recurrence equations
under Kesten's condition. Ann. Probab. 41, 2755-2790.
See here.
Mikosch, T. and Wintenberger, O. (2013)
Precise large deviations for dependent regularly
varying sequences. Probab. Th.
Rel. Fields. 156, 851-887.
here.
Mikosch, T., Vries, C. de. (2013)
Heavy tails of OLS. J.
Econometrics 172, 205-221.
See here.
Matsui, M., Mikosch, T. and Tafakori, L. (2013)
Estimation of the
tail index for lattice-valued sequences. Extremes 16, 429-455.
See here.
Mikosch, T., Tafakori, L. and Samorodnitsky, G. (2013)
Fractional moments of solutions to stochastic recurrence equations.
J. Appl. Probab. 50, 969-982.
See here.
Davis, R.A., Mikosch, T. and Zhao, Y. (2013)
Measures of serial extremal dependence and their estimation.
Stoch. Proc. Appl. 123, 2575-2602.
See here.
**
2014
**

Mikosch, T. and Zhao, Y. (2014)
A Fourier analysis of extreme events. Bernoulli 20, 803-845.
See here.
Mikosch, T. and Wintenberger, O. (2014)
The cluster index of regularly varying sequences with applications to
limit theory for functions of multivariate Markov chains.
Probab. Th.
Rel. Fields 159, 157-196. See
here.
Damek, E., Mikosch, T., Rosinski, J. and Samorodnitsky, G. (2014)
Inverse problems for regular variation.
J. Appl. Probab. 51A, 229-248.. See
here.
Hashorva, E., Mikosch, T. and Embrechts, P. (2014)
Aggregation of log-linear risks.
J. Appl. Probab., 51A, 203-212. See
here.
**
2015
**

Mikosch, T. and Zhao, Y. (2015)
The integrated periodogram of a dependent extremal event sequence.
Stoch. Proc. Applic., 125, 3126-3169. See here.
Dieker, T. and Mikosch, T. (2015)
Exact simulation of a Brown-Resnick random field.
Extremes, 18, 301-314. See here.
**
2016
**

Matsui, M, and Mikosch, T. (2016)
The extremogram and the cross-extremogram for a bivariate GARCH(1,1) process.
Adv. Appl. Probab. Special Issue (Nick Bingham Festschrift, Eds. C. Goldie
and A. Mijatovic) 48A, 217-233.
See here.
Davis, R.A., Mikosch, T. and Pfaffel, O. (2016)
Asymptotic theory for the sample covariance matrix of a heavy-tailed
multivariate time series.
Stoch. Proc. Appl. 126, 767-799.
See here.
Davis, R.A., Heiny, J., Mikosch, T. and Xie, X. (2016)
Extreme value analysis for the sample
autocovariance matrices of heavy-tailed multivariate time series.
Extremes, 19, 517-547.
See here.
Mikosch, T. and Wintenberger, O. (2016)
A large deviations approach to limit theory for heavy-tailed time series.
Probab. Th. Rel. Fields, 166, 233-269.
See here.
**
2017
**

Heiny, J. and Mikosch, T. (2017)
Eigenvalues and eigenvectors of heavy-tailed sample
covariance matrices with general growth rates: the iid
case. Stoch. Proc. Appl. 127, 2179-2242.
See here.
Matsui, M., Mikosch, T. and Samorodnitsky, G. (2017)
Distance covariance for stochastic processes. Probab. Math. Statistics, 37, 355-372.
See here.
**
2018
**

Janssen, A., Mikosch, T., Rezapour, M. and Xie, X. (2018)
The eigenvalues of the sample covariance matrix of a
multivariate heavy-tailed stochastic volatility model. Bernoulli, 24, 1351-1393.
See here.
Heiny, J. and Mikosch, T. (2018)
Almost sure convergence of the largest and smallest
eigenvalues of high-dimensional sample correlation
matrices. Stoch. Proc. Appl., 128, 2779-2815.
See here.
Davis, R.A., M. Matsui, Mikosch, T. and Wan, P. (2018)
Applications of distance correlation to time series.
Bernoulli, 24, 3087-3116.
See here.
and here.
**
2019
**

Mikosch, T. Rezapour, M. and Wintenberger, O. (2019)
Heavy tails for an alternative stochastic perpetuity model. Stoch. Proc. Appl., 129, 4638-4662.
See here.
Liu, Z., Blanchet, J., Dieker, T. and Mikosch, T. (2019)
On logarithmically optimal exact simulation of max-stable and
related random fields on a compact set. Bernoulli, 25, 3590â3622.
See here.
Heiny, J. and Mikosch, T. (2019)
The eigenstructure of the sample covariance matrices of high-dimensional stochastic volatility models with heavy tails. Bernoulli, 25, 2949â2981.
See here.
**
2020**

Dyszewski, P. and Mikosch, T. (2020)
Homogeneous mappings of regularly varying vectors.
Ann. Appl. Probab. 30, 2999-3026.
See here.
Dehling, H., Matsui, M., Mikosch, T., Samorodnitsky, G. and Tafakori, L. (2020)
Distance covariance for discretized stochastic processes. Bernoulli 26, 2758-2789.
See here.
Mikosch, T. and Yslas, J. (2020)
Gumbel and Frechet convergence of the maxima of independent random walks. Adv.
Appl. Probab. 52, 213-236.
See here.
**
2021
**

Heiny, J. and Mikosch, T. (2021)
Large sample autocovariance matrices of linear processes with heavy tails.
Stoch. Proc. Appl. 141, 344-375.
See here.
Mikosch, T. and Rodionov, I. (2021)
Precise large deviations for dependent subexponential variables.
Bernoulli 27, 1319-1349.
See here.
Heiny, J., Mikosch, T. and Yslas, J. (2021)
Point process convergence for the off-diagonal entries of sample covariance
matrices. Ann. Appl. Probab. 31, 538-560.
See here.
Buritica, G., Meyer, N., Mikosch, T. and Wintenberger, O. (2021)
Some variations on the extremal index. (In Russian). Zap. Nauchn. Sem. POMI
501, Probability and Statistics (2021) 30, 52-77. The English version
will appear in J. Math. Sci. (Springer).
See here.
**
2022
**

Matsui, M., Mikosch, T. Tafakori, L. and Roozegar, R. (2022)
Distance covariance for random fields. Stoch. Proc. Appl.
150, 280-322.
See here.
**
2023
**

Damek, E., Mikosch, T., Zhao, Y. and Zienkiewicz, J. (2023)
Whittle estimation based on the extremal spectral density of a heavy-tailed random field.
Stoch. Proc. Appl. 155, 232-267.
ee here.