Multiplicative strong unimodality for positive stable laws

2010/02/26 by Thomas Simon, Simon, Thomas · 1 citation
Decision Sciences · Economics, Econometrics and Finance · #60E07 #60E15 #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications

paper · doi:10.48550/arxiv.1002.4977

openalex publication_date 2010/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is known that real Non-Gaussian stable distributions are unimodal, not additive strongly unimodal, and multiplicative strongly unimodal in the symmetric case. By a theorem of Cuculescu-Theodorescu, the only remaining relevant situation for the multiplicative strong unimodality of stable laws is the one-sided. In this paper, we show that positive α-stable laws are multiplicative strongly unimodal iff α≤ 1/2.

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