Partition-dependent stochastic measures and -deformed cumulants

  • Michael Anshelevich

    Department of Mathematics University of California Berkeley, CA 94720
Partition-dependent stochastic measures and $q$-deformed cumulants cover
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On a -deformed Fock space, we define multiple -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 -convolution for a large class of probability measures. We make some comments on the Itô table in this context, and investigate the -Brownian motion and the -Poisson process in more detail.

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Michael Anshelevich, Partition-dependent stochastic measures and -deformed cumulants. Doc. Math. 6 (2001), pp. 343–384

DOI 10.4171/DM/106