The Hidden Regular Variation in the 21st Century Resnick, Sidney. creator author. aut http://id.loc.gov/vocabulary/relators/aut SpringerLink (Online service) text sz 2024 1st ed. 2024. monographic eng

electronic

electronic resource

access XIII, 262 p. 105 illus., 73 illus. in color. online resource. 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. 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. by Sidney Resnick. Stochastic processes Probabilities Stochastic Processes Applied Probability QA274-274.9 9783031575990 https://doi.org/10.1007/978-3-031-57599-0 https://doi.org/10.1007/978-3-031-57599-0 240802 20251030112706.0 978-3-031-57599-0