An infinite-dimensional analogue of the Lebesgue measure and distinguished properties of the gamma process
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Publication:5949557
DOI10.1006/jfan.2001.3767zbMath0990.60053OpenAlexW2013187140WikidataQ104243772 ScholiaQ104243772MaRDI QIDQ5949557
Natalia V. Tsilevich, Marc Yor, Anatoly M. Vershik
Publication date: 1 August 2002
Published in: Journal of Functional Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1006/jfan.2001.3767
Processes with independent increments; Lévy processes (60G51) Stable stochastic processes (60G52) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20)
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A commutative model of presentation of the group of flows \(SL(2,R)^ X\) that is connected with a unipotent subgroup
- Completely random measures
- Factorizable representation of current algebra. Non commutative extension of the Levy-Kinchin formula and cohomology of a solvable group with values in a Hilbert space
- A Bayesian analysis of some nonparametric problems
- Quasi-invariance of the gamma process and multiplicative properties of the Poisson-Dirichlet measures
- Poisson Measures Quasi-Invariant with Respect to Multiplicative Transformations
- A Representation of Independent Increment Processes without Gaussian Components
- A Characterization of the Gamma Distribution
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