03073nam a22005175i 4500 978-3-031-57599-0 DE-He213 20251030112706.0 cr nn 008mamaa 240802s2024 sz | s |||| 0|eng d 9783031575990 978-3-031-57599-0 10.1007/978-3-031-57599-0 doi QA274-274.9 PBT bicssc PBWL bicssc MAT029040 bisacsh PBT thema PBWL thema Resnick, Sidney. author. aut http://id.loc.gov/vocabulary/relators/aut 81783 The Art of Finding Hidden Risks [electronic resource] : Hidden Regular Variation in the 21st Century / by Sidney Resnick. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. XIII, 262 p. 105 illus., 73 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda 1 Foundation -- 2 Regular Variation -- 3 Hidden Regular Variation -- 4 Lévy Processes with Regularly Varying Distributions: Where Do the Jumps Go? -- 5 Statistics -- A A Crash Course on Regularly Varying Functions -- B Notation Summary -- References -- Index. This text gives a comprehensive, largely self-contained treatment of multivariate heavy tail analysis. Emphasizing regular variation of measures means theory can be presented systematically and without regard to dimension. Tools are developed that allow a flexible definition of "extreme" in higher dimensions and permit different heavy tails to coexist on the same state space leading to "hidden regular variation" and "steroidal regular variation". This emphasizes when estimating risks, it is important to choose the appropriate heavy tail. Theoretical foundations lead naturally to statistical techniques; examples are drawn from risk estimation, finance, climatology and network analysis. Treatments target a broad audience in insurance, finance, data analysis, network science and probability modeling. The prerequisites are modest knowledge of analysis and familiarity with the definition of a measure; regular variation of functions is reviewed but is not a focal point. Stochastic processes. 76770 Probabilities. 65724 Stochastic Processes. 76770 Applied Probability. 65727 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031575983 Printed edition: 9783031576003 Printed edition: 9783031576010 https://doi.org/10.1007/978-3-031-57599-0 ZDB-2-SMA ZDB-2-SXMS 62171 62171