Geodesic
Partition-dependent stochastic measures and $q$-deformed cumulants
Documenta mathematica, Tome 6 (2001), pp. 343-384.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: On a $q$-deformed Fock space, we define multiple $q$-Lévy processes. Using the partition-dependent stochastic measures derived from such processes, we define partition-dependent cumulants for their joint distributions, and express these in terms of the cumulant functional using the number of restricted crossings of P. Biane. In the single variable case, this allows us to define a $q$-convolution for a large class of probability measures. We make some comments on the Itô table in this context, and investigate the $q$-Brownian motion and the $q$-Poisson process in more detail.
Classification : 46L53, 05A18, 47D, 60E, 81S05 
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     author = {Anshelevich, Michael},
     title = {Partition-dependent stochastic measures and $q$-deformed cumulants},
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     volume = {6},
     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2001__6__a8/}
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Anshelevich, Michael. Partition-dependent stochastic measures and $q$-deformed cumulants. Documenta mathematica, Tome 6 (2001), pp. 343-384. http://geodesic.mathdoc.fr/item/DOCMA_2001__6__a8/