Ratio of the tail of an infinitely divisible distribution on the line to that of its Lévy measure
Toshiro Watanabe, University of Aizu
Kouji Yamamuro, Gifu University
Abstract
A necessary and sufficient condition for
the tail of an infinitely divisible distribution on the real line
to be estimated by
the tail of its Lévy measure is found. The lower limit
and the upper limit of the ratio
of the right tail μ(r) of an infinitely divisible
distribution μ to the right tail ν(r) of its Lévy
measure ν as r → ∞ are estimated from above and below
by reviving Teugels's classical method. The exponential
class and the dominated varying class are studied in detail.
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