MONOTONE CONVOLUTION AND MONOTONE INFINITE DIVISIBILITY FROM COMPLEX ANALYTIC VIEWPOINT

DOI10.1142/S0219025710003973zbMath1198.60014OpenAlexW2141440101MaRDI QIDQ3560054

Takahiro Hasebe

Publication date: 19 May 2010

Published in: Infinite Dimensional Analysis, Quantum Probability and Related Topics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219025710003973

zbMATH Keywords

monotone convolutionInfinite divisibility

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Characteristic functions; other transforms (60E10) Denjoy and Perron integrals, other special integrals (26A39)

Related Items (16)

A note on the rate of convergence in the Boolean central limit theorem ⋮ Tree convolution for probability distributions with unbounded support ⋮ On a class of explicit Cauchy-Stieltjes transforms related to monotone stable and free Poisson laws ⋮ Strict limit types for monotone convolution ⋮ Quantum Probability Aspects to Lexicographic and Strong Products of Graphs ⋮ FOURIER AND CAUCHY–STIELTJES TRANSFORMS OF POWER LAWS INCLUDING STABLE DISTRIBUTIONS ⋮ Unimodality of Boolean and monotone stable distributions ⋮ Analytic continuations of Fourier and Stieltjes transforms and generalized moments of probability measures ⋮ Classical scale mixtures of Boolean stable laws ⋮ Subordination methods for free deconvolution ⋮ Operator-valued chordal Loewner chains and non-commutative probability ⋮ CONDITIONALLY MONOTONE INDEPENDENCE I: INDEPENDENCE, ADDITIVE CONVOLUTIONS AND RELATED CONVOLUTIONS ⋮ On a Berry-Esseen type limit theorem for Boolean convolution ⋮ Monotone increment processes, classical Markov processes, and Loewner chains ⋮ An operad of non-commutative independences defined by trees ⋮ Free subordination and Belinschi-Nica semigroup

Cites Work

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• Addition of freely independent random variables
• Noncommutative Brownian motion in monotone Fock space
• THE MAIN RESULTS ON SUFFICIENT CONDITIONS FOR AN ANALYTIC FUNCTION TO BE SCHLICHT
• MONOTONIC INDEPENDENCE, MONOTONIC CENTRAL LIMIT THEOREM AND MONOTONIC LAW OF SMALL NUMBERS
• Monotone and boolean convolutions for non-compactly supported probability measures

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