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, 3590–3622. 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, 2949–2981. 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.