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Contents of PMS, Vol. 33, Fasc. 2,
pages 363 - 375
 

ON FREE INFINITE DIVISIBILITY FOR CLASSICAL MEIXNER DISTRIBUTIONS

Marek Bożejko
Takahiro Hasebe

Abstract: We prove that symmetric Meixner distributions, whose probability densities are proportional to |Γ (t+ ix)|2  , are freely infinitely divisible for 0 < t ≤ 1
       2  . The case t = 1
   2  corresponds to the law of Lévy’s stochastic area whose probability density is 1∕cosh (πx ) . A logistic distribution, whose probability density is proportional to 1∕cosh2(πx) , is also freely infinitely divisible.

2000 AMS Mathematics Subject Classification: Primary: 46L54; Secondary: 30C45.

Keywords and phrases: Meixner distribution, Lévy’s stochastic area, logistic distribution, free infinite divisibility.

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