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On the Strong Unimodality of Lévy Processes

Published online by Cambridge University Press:  22 January 2016

Toshiro Watanabe
Toshiro Watanabe*
Affiliation:
Nakamandokoro, Aizubangemachi, Fukushima-ken, 969-65, Japan
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A measure μ(dx) on R is said to be unimodal with mode a if μ(dx) = cδa(dx) + f(x) dx, where c ≧ 0, δa(dx) is the delta measure at a and f(x) is non-decreasing for x < a and non-increasing for x > a. A measure is said to be unimodal with mode a if pn is non-decreasing for n ≦ a and non-increasing for n ≧ a. A probability measure μ(dx) on R (resp. on Z) is said to be strongly unimodal on R (resp. on Z) if, for every unimodal probability measure η(dx) on R (resp. on Z), the convolution μ*η(dx) is unimodal on R (resp. on Z).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 121 , March 1991 , pp. 195 - 199
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1991

References

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