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1

Kulik, Rafal, and Philippe Soulier. Heavy-Tailed Time Series. Springer New York, 2020. http://dx.doi.org/10.1007/978-1-0716-0737-4.

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2

Laha, Arnab Kumar. Portfolio allocation with heavy-tailed returns. Indian Institute of Management, 2005.

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3

Pisarenko, V., and M. Rodkin. Heavy-Tailed Distributions in Disaster Analysis. Springer Netherlands, 2010. http://dx.doi.org/10.1007/978-90-481-9171-0.

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4

Peters, Gareth W., and Pavel V. Shevchenko. Advances in Heavy Tailed Risk Modeling. John Wiley & Sons, Inc, 2015. http://dx.doi.org/10.1002/9781118909560.

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5

name, No. Handbook of heavy tailed distributions in finance. Elsevier, 2002.

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6

Dmitry, Korshunov, Zachary Stan, and SpringerLink (Online service), eds. An Introduction to Heavy-Tailed and Subexponential Distributions. Springer Science+Business Media, LLC, 2011.

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Foss, Sergey, Dmitry Korshunov, and Stan Zachary. An Introduction to Heavy-Tailed and Subexponential Distributions. Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-7101-1.

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8

Foss, Sergey, Dmitry Korshunov, and Stan Zachary. An Introduction to Heavy-Tailed and Subexponential Distributions. Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4419-9473-8.

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9

Ibragimov, Marat, Rustam Ibragimov, and Johan Walden. Heavy-Tailed Distributions and Robustness in Economics and Finance. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-16877-7.

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10

Markovich, Natalia. Nonparametric analysis of univariate heavy-tailed data: Research and practice. John Wiley & Sons, 2007.

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11

Wright, Jonathan H. Log-periodogram estimation of long memory volatility dependencies with conditionally heavy tailed returns. Federal Reserve Board, 2000.

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12

Soulier, Philippe, and Rafal Kulik. Heavy-Tailed Time Series. Springer, 2020.

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13

Kravtsov, Vladimir. Heavy-tailed random matrices. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.13.

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This article considers non-Gaussian random matrices consisting of random variables with heavy-tailed probability distributions. In probability theory heavy tails of distributions describe rare but violent events which usually have a dominant influence on the statistics. Furthermore, they completely change the universal properties of eigenvalues and eigenvectors of random matrices. This article focuses on the universal macroscopic properties of Wigner matrices belonging to the Lévy basin of attraction, matrices representing stable free random variables, and a class of heavy-tailed matrices obta
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14

Inference for Heavy-Tailed Data Analysis. Elsevier, 2017. http://dx.doi.org/10.1016/c2015-0-01492-7.

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15

T, Rachev S., ed. Handbook of heavy tailed distributions in finance. Elsevier, 2003.

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16

Handbook of Heavy Tailed Distributions in Finance. Elsevier, 2003. http://dx.doi.org/10.1016/b978-0-444-50896-6.x5000-6.

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17

Foss, Sergey, Dmitry Korshunov, and Stan Zachary. An Introduction to Heavy-Tailed and Subexponential Distributions. Springer, 2011.

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18

Foss, Sergey, Dmitry Korshunov, and Stan Zachary. An Introduction to Heavy-Tailed and Subexponential Distributions. Springer, 2013.

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19

Foss, Sergey, Dmitry Korshunov, and Stan Zachary. An Introduction to Heavy-Tailed and Subexponential Distributions. Springer, 2015.

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20

Ibragimov, Rustam, Marat Ibragimov, and Johan Walden. Heavy-Tailed Distributions and Robustness in Economics and Finance. Springer, 2015.

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21

Markovich, Natalia. Nonparametric Analysis of Univariate Heavy-Tailed Data: Research and Practice. Wiley & Sons, Incorporated, John, 2008.

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22

Shevchenko, Pavel V., and Gareth W. Peters. Advances in Heavy Tailed Risk Modeling: A Handbook of Operational Risk. Wiley & Sons, Incorporated, John, 2015.

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23

Advances in Heavy Tailed Risk Modeling: A Handbook of Operational Risk. Wiley & Sons, Incorporated, John, 2015.

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24

Bianchi, Michele Leonardo, Stoyan V. Stoyanov, Gian Luca Tassinari, Frank J. Fabozzi, and Sergio M. Focardi. Handbook of Heavy-Tailed Distributions in Asset Management and Risk Management. WORLD SCIENTIFIC, 2019. http://dx.doi.org/10.1142/11118.

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25

Peng, Liang, and Yongcheng Qi. Inference for Heavy-Tailed Data Analysis: Applications in Insurance and Finance. Elsevier Science & Technology Books, 2017.

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26

Fabozzi, Frank J., Michele Leonardo Bianchi, Stoyan V. Stoyanov, Gian Luca Tassinari, and Sergio M. Focardi. Handbook of Heavy-Tailed Distributions in Asset Management and Risk Management. World Scientific Publishing Co, 2019.

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27

Asymptotic Analysis of Random Walks: Heavy-Tailed Distributions (Encyclopedia of Mathematics and its Applications). Cambridge University Press, 2008.

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28

Markovich, Natalia. Nonparametric Analysis of Univariate Heavy-Tailed Data: Research and Practice (Wiley Series in Probability and Statistics). Wiley-Interscience, 2007.

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29

Thurner, Stefan, Rudolf Hanel, and Peter Klimekl. Probability and Random Processes. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198821939.003.0002.

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Phenomena, systems, and processes are rarely purely deterministic, but contain stochastic,probabilistic, or random components. For that reason, a probabilistic descriptionof most phenomena is necessary. Probability theory provides us with the tools for thistask. Here, we provide a crash course on the most important notions of probabilityand random processes, such as odds, probability, expectation, variance, and so on. Wedescribe the most elementary stochastic event—the trial—and develop the notion of urnmodels. We discuss basic facts about random variables and the elementary operationsthat can
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