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pro vyhledávání: '"Schürmann, Michael"'
Autor:
Schürmann, Michael
This article is on the research of Wilhelm von Waldenfels in the mathematical field of quantum (or non-commutative) probability theory. Wilhelm von Waldenfels was one of the pioneers, even one of the founders, of quantum probability. We concentrate o
Externí odkaz:
http://arxiv.org/abs/2207.05540
Publikováno v:
SIGMA 18 (2022), 075, 27 pages
We generalize Franz' independence in tensor categories with inclusions from two morphisms (which represent generalized random variables) to arbitrary ordered families of morphisms. We will see that this only works consistently if the unit object is a
Externí odkaz:
http://arxiv.org/abs/1612.05139
Autor:
Manzel, Sarah, Schürmann, Michael
In a central lemma we characterize "generating functions" of certain functors on the category of algebraic non-commutative probability spaces. Special families of such generating functions correspond to "unital, associative universal products" on thi
Externí odkaz:
http://arxiv.org/abs/1601.06779
Autor:
Schürmann, Michael, Voß, Stefan
As in the classical case of L\'evy processes on a group, L\'evy processes on a Voiculescu dual group are constructed from conditionally positive functionals. It is essential for this construction that Schoenberg correspondence holds for dual groups:
Externí odkaz:
http://arxiv.org/abs/1210.1830
Publikováno v:
Commun. Stoch. Anal. 4 (553-577) 2010
A L\'evy process on a *-bialgebra is given by its generator, a conditionally positive hermitian linear functional vanishing at the unit element. A *-algebra homomorphism k from a *-bialgebra C to a *-bialgebra B with the property that k respects the
Externí odkaz:
http://arxiv.org/abs/0712.3504
The aim of this article is to characterize unitary increment process by a quantum stochastic integral representation on symmetric Fock space. Under certain assumptions we have proved its unitary equivalence to a Hudson-Parthasarathy flow.
Commen
Commen
Externí odkaz:
http://arxiv.org/abs/0712.1896
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Publikováno v:
SIGMA. Symmetry, Integrability and Geometry
We generalize Franz' independence in tensor categories with inclusions from two morphisms (which represent generalized random variables) to arbitrary ordered families of morphisms. We will see that this only works consistently if the unit object is a
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3497827aa91a3994ae355e6b38cca2b5
https://doi.org/10.3842/sigma.2022.075
https://doi.org/10.3842/sigma.2022.075
(Quantum) stochastic processes with independent and stationary increments (i.e. Lévy processes) and in particular Brownian motions in braided monoidal categories are studied. The notion of increments is based on a bialgebra or Hopf algebra structure
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=od_______166::1c6daf00dcae2921848bb75a96aa2d30
https://hal.archives-ouvertes.fr/hal-03664273
https://hal.archives-ouvertes.fr/hal-03664273