TY - JOUR
T1 - Strong Laws of Large Numbers for Intermediately Trimmed Sums of i.i.d. Random Variables with Infinite Mean
AU - Kesseböhmer, Marc
AU - Schindler, Tanja
N1 - Publisher Copyright:
© 2017, Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2019/6/1
Y1 - 2019/6/1
N2 - We show that for every sequence of nonnegative i.i.d. random variables with infinite mean there exists a proper moderate trimming such that for the trimmed sum process a non-trivial strong law of large numbers holds. We provide an explicit procedure to find a moderate trimming sequence even if the underlying distribution function has a complicated structure, e.g., has no regularly varying tail distribution.
AB - We show that for every sequence of nonnegative i.i.d. random variables with infinite mean there exists a proper moderate trimming such that for the trimmed sum process a non-trivial strong law of large numbers holds. We provide an explicit procedure to find a moderate trimming sequence even if the underlying distribution function has a complicated structure, e.g., has no regularly varying tail distribution.
KW - Almost sure convergence theorem
KW - Moderately trimmed sum
KW - Strong law of large numbers
UR - http://www.scopus.com/inward/record.url?scp=85038077510&partnerID=8YFLogxK
U2 - 10.1007/s10959-017-0802-0
DO - 10.1007/s10959-017-0802-0
M3 - Article
SN - 0894-9840
VL - 32
SP - 702
EP - 720
JO - Journal of Theoretical Probability
JF - Journal of Theoretical Probability
IS - 2
ER -