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Understanding Heavy Tails in a Bounded World or, is a Truncated Heavy Tail Heavy or Not? [PDF]

open access: yesStochastic Models, 2012
We address the important question of the extent to which random variables and vectors with truncated power tails retain the characteristic features of random variables and vectors with power tails. We define two truncation regimes, soft truncation regime and hard truncation regime, and show that, in the soft truncation regime, truncated power tails ...
Arijit Chakrabarty   +1 more
exaly   +3 more sources
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HARCH Processes are Heavy Tailed

Extremes, 1999
A \(\text{HARCH}(k)\) process \(R_n\) is defined by the recursive relations \[ R_n=\sigma_n\varepsilon_n, \qquad \sigma_n^2=c_0+\sum_{j=1}^kc_j \left( \sum_{i=1}^j R_{n-i} \right)^2 \] where the \(c_j\) are some nonrandom constants, \(\varepsilon_n\) are i.i.d., \(E\varepsilon=0\), \(E\varepsilon^20\) and \(\Pr(\varepsilon^2>c_1^{-1})>0\), then ...
Embrechts, Paul, GrĂ¼bel, Rudolf
openaire   +2 more sources

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