Monotone and boolean convolutions for non-compactly supported probability measures

DOI10.1512/iumj.2009.58.3578zbMath1186.46065arXivmath/0703408OpenAlexW2950454815MaRDI QIDQ5325389

Uwe Franz

Publication date: 10 August 2009

Published in: Indiana University Mathematics Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0703408

zbMATH Keywords

unbounded operatorsBoolean independencemonotone independenceBoolean convolutionmonotone convolution

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Free probability and free operator algebras (46L54) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Noncommutative probability and statistics (46L53)

Related Items (16)

Relations between convolutions and transforms in operator-valued free probability ⋮ On operator-valued monotone independence ⋮ Conditionally monotone independence II: multiplicative convolutions and infinite divisibility ⋮ Generators of some non-commutative stochastic processes ⋮ Extended de Finetti theorems for boolean independence and monotone independence ⋮ Strict limit types for monotone convolution ⋮ MONOTONE CONVOLUTION AND MONOTONE INFINITE DIVISIBILITY FROM COMPLEX ANALYTIC VIEWPOINT ⋮ Limit theorems for free Lévy processes ⋮ Boolean convolutions and regular variation ⋮ Classical scale mixtures of Boolean stable laws ⋮ Loewner's differential equation and spidernets ⋮ A noncommutative de Finetti theorem for Boolean independence ⋮ CONDITIONALLY MONOTONE INDEPENDENCE I: INDEPENDENCE, ADDITIVE CONVOLUTIONS AND RELATED CONVOLUTIONS ⋮ Monotone increment processes, classical Markov processes, and Loewner chains ⋮ An operad of non-commutative independences defined by trees ⋮ Free subordination and Belinschi-Nica semigroup

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