June 2024: Extreme Value Theory
Extreme value theory concerns the probabilities of extreme and rare events. An important example is the asymptotic behaviour of the maxima of increasing collections of random variables. The classical situation of i.i.d. random variables is studied in the famous Fisher-Tippett-Gnedenko theorem, but one can also consider dependent random variables or take the maxima of collections of random vectors or stochastic processes. Further problems include tail probabilities and the behaviour of a random vector or stochastic process conditioned on some quantity being large. Regular variation and related concepts play a key role in extreme value theory. Extremes are also investigated in other branches of probability theory such as random graphs or stochastic geometry. Extreme value theory is applied in diverse fields ranging from meteorology and environmental science over life sciences to finance and insurance, where, for example, one is interested in modelling risks or computing ruin probabilities.
Collection created by Matthias Schulte (Hamburg University of Technology)
Original Article
Limit laws for large
$k$ th-nearest neighbor balls
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- Journal of Applied Probability / Volume 59 / Issue 3 / September 2022
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- 06 July 2022, pp. 880-894
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Linking representations for multivariate extremes via a limit set
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- Advances in Applied Probability / Volume 54 / Issue 3 / September 2022
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- 13 June 2022, pp. 688-717
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Research Papers
Simultaneous ruin probability for two-dimensional brownian risk model
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- Journal of Applied Probability / Volume 57 / Issue 2 / 2020
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- 16 July 2020, pp. 597-612
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Research Article
Markov Tail Chains
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- Journal of Applied Probability / Volume 51 / Issue 4 / December 2014
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- 30 January 2018, pp. 1133-1153
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Short Communications
On the rate of convergence of normal extremes
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- Journal of Applied Probability / Volume 16 / Issue 2 / June 1979
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- 14 July 2016, pp. 433-439
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General Applied Probability
Concomitant tail behaviour for extremes
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- Advances in Applied Probability / Volume 30 / Issue 1 / 1998
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- 01 July 2016, pp. 197-215
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Part 5. Finance and econometrics
Aggregation of log-linear risks
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- Journal of Applied Probability / Volume 51 / Issue A / 2014
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- 30 March 2016, pp. 203-212
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Research Papers
Nonstandard regular variation of in-degree and out-degree in the preferential attachment model
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- Journal of Applied Probability / Volume 53 / Issue 1 / March 2016
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- 24 March 2016, pp. 146-161
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General Applied Probability
Statistical Inference for Max-Stable Processes by Conditioning on Extreme Events
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- Advances in Applied Probability / Volume 46 / Issue 2 / 2014
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- 22 February 2016, pp. 478-495
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Living on the Multidimensional Edge: Seeking Hidden Risks Using Regular Variation
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- Advances in Applied Probability / Volume 45 / Issue 1 / 2013
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- 04 January 2016, pp. 139-163
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