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2015 | Vol. 48, nr 3 | 424--439
Tytuł artykułu

Unimodality of Boolean and monotone stable distributions

Wybrane pełne teksty z tego czasopisma
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We give a complete list of the Lebesgue–Jordan decomposition of Boolean and monotone stable distributions and a complete list of the mode of them. They are not always unimodal.
Wydawca

Rocznik
Strony
424--439
Opis fizyczny
Bibliogr. 18 poz., wykr.
Twórcy
autor
  • Laboratoire de Mathématiques, Université de Franche-Comté 16 Route de Gray, 25030 Besançon Cedex, France, thasebe@math.sci.hokudai.ac.jp
  • Department of Mathematics, Hokkaido University, Kita 10, Nishi 8 Kita-Ku, Sapporo 060-0810, Japan
autor
  • Department of Mathematics, Aichi University of Education, 1 Hirosawa, Igaya-Cho, Kariya-Shi, 448-8542, Japan, sakuma@auecc.aichi-edu.ac.jp
Bibliografia
  • [1] N. I. Akhiezer, The Classical Moment Problem, Oliver and Boyd, Edinburgh, 1965.
  • [2] M. Anshelevich, J. D. Williams, Limit theorems for monotonic convolution and the Chernoff product formula, Int. Math. Res. Not. 11 (2014), 2990–3021.
  • [3] O. Arizmendi, T. Hasebe, On a class of explicit Cauchy–Stieltjes transforms related to monotone stable and free Poisson laws, Bernoulli 19(5B) (2013), 2750–2767.
  • [4] O. Arizmendi, T. Hasebe, Classical and free infinite divisibility for Boolean stable laws, Proc. Amer. Math. Soc. 142 (2014), 1621–1632.
  • [5] H. Bercovici, V. Pata, Stable laws and domains of attraction in free probability theory (with an appendix by P. Biane), Ann. of Math. (2) 149 (1999), 1023–1060.
  • [6] P. Biane, Processes with free increments, Math. Z. 227 (1998), 143–174.
  • [7] T. Hasebe, Monotone convolution and monotone infinite divisibility from complex analytic viewpoints, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 13(1) (2010), 111–131.
  • [8] T. Hasebe, Monotone convolution semigroups, Studia Math. 200(2) (2010), 175–199.
  • [9] T. Hasebe, A. Kuznetsov, On free stable distributions, Electron. Comm. Probab. 19 (2014), 12 pp.
  • [10] T. Hasebe, S. Thorbjørnsen, Unimodality of the freely selfdecomposable probability laws. arXiv:1309:6776
  • [11] N. Muraki, Monotonic convolution and monotonic Lévy–Hinčin formula, preprint, 2000.
  • [12] N. Muraki,Monotonic independence, monotonic central limit theorem and monotonic law of small numbers, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 4 (2001), 39–58.
  • [13] K. Sato, Lévy processes and infinitely divisible distributions, Translated from the 1990 Japanese original, Revised by the author, Cambridge Studies in Advanced Mathematics, 68, Cambridge University Press, Cambridge, 1999.
  • [14] R. Speicher, R. Woroudi, Boolean convolution, Free Probability Theory, Ed. D. Voiculescu, Fields Inst. Commun., vol. 12, American Mathematical Society, Providence, RI, 1997, 267–280.
  • [15] G. Teschl, Jacobi Operators and Completely Integrable Nonlinear Lattices, Mathematical Surveys and Monographs 72, American Mathematical Society, Providence, RI, 2000.
  • [16] J.-C. Wang, Strict limit types for monotone convolution, J. Funct. Anal. 262(1) (2012), 35–58.
  • [17] M. Yamazato, Unimodality of infinitely divisible distribution functions of class L, Ann. Probab. 6 (1978), 523–531.
  • [18] V. M. Zolotarev, One-dimensional stable distributions , vol. 65, Translations of Mathematical Monographs, American Mathematical Society, Providence, RI, 1986.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
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