On the Rate of Convergence in Extreme Value Theory

1989 ◽  
Vol 33 (3) ◽  
pp. 560-566 ◽  
Author(s):  
E. Omey ◽  
S. Rachev
Keyword(s):  
Rate Of Convergence ◽  
Extreme Value Theory ◽  
Value Theory ◽  
Extreme Value

scholarly journals Continued fractions, the Chen–Stein method and extreme value theory

2019 ◽  
Vol 41 (2) ◽  
pp. 461-470
Author(s):  
ANISH GHOSH ◽  
MAXIM SØLUND KIRSEBOM ◽  
PARTHANIL ROY
Keyword(s):  
Rate Of Convergence ◽  
Extreme Value Theory ◽  
Upper Bound ◽  
Continued Fractions ◽  
Continued Fraction ◽  
Value Theory ◽  
Extreme Value ◽  
Real Analysis ◽  
Continued Fraction Expansion ◽  
Stein Method

In this work we deal with extreme value theory in the context of continued fractions using techniques from probability theory, ergodic theory and real analysis. We give an upper bound for the rate of convergence in the Doeblin–Iosifescu asymptotics for the exceedances of digits obtained from the regular continued fraction expansion of a number chosen randomly from $(0,1)$ according to the Gauss measure. As a consequence, we significantly improve the best known upper bound on the rate of convergence of the maxima in this case. We observe that the asymptotics of order statistics and the extremal point process can also be investigated using our methods.

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