Partition-dependent stochastic measures and $q$-deformed cumulants

By Michael Anshelevich. Documenta Mathematica, 2001

61 citations recorded by the source corpus.

On a q-deformed Fock space, we deflne multiple q-L¶ processes. Using the partition-dependent stochastic measures derived from such processes, we deflne partition-dependent cumulants for their joint distributions, and express these in terms of the cumulant func- tional using the number of restricted crossings of P. Biane. In the single variable case, this allows us to deflne a q-convolution for a large class of probability measures. We make some comments on the It^o table in this context, and investigate the q-Brownian motion and the q-Poisson process in more detail.

Subfields: Algebra and Number Theory, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/775386fd39a5346abd80cac649bde17a850f0d26

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

In Mathematical Physics

In Statistics and Probability

Citations in the corpus

Self-decomposability and Lévy processes in free probability (2002, methodology): “(Stochastic integration (of processes) with respect to free Lévy pro- cesses has also, in recent independent work, been introduced by Anshelevich (2001a), using a quite different technique.”
On a class of free Lévy laws related to a regression problem (2004, methodology): “recurrence R n+1 = aR n + b nX−1 j=2 n− 1 j − 1 q R jR n+1−j, n ≥ 2, (25) with the initial values R1 = 0,R2 = 1. Here we use the standard notation [n] q = 1 + q + ...+ qn−1, [n] q! = [1] q[2] q ...[n] q, n k q = [n] q! [n −k] q![k] q! , with the usual conventions [0] q = 0,[0] q! = 1. Th”
Appell polynomials and their relatives (2003, background): “4 q-Kailath-Segall polynomials The origin of these polynomials is in the q-Lévy processes defined in [6, 9].”
Monoidal Functors, Species, and Hopf Algebras (2010, methodology): “L left adjoint of a Fock functor 588 R right adjoint of a Fock functor 587 Q right adjoint of a Fock functor 591 R right adjoint of a Fock functor 583 Q right adjoint of a Fock functor 591 L∨ right adjoint of a Fock functor 588 R∨ left adjoint of a Fock functor 597 Q∨ left adjoint of a Fock functor ”