18 citations · 78 across the 23 of their papers we have counts for
4 papers · 2 filters
Filtered random variables, bialgebras and convolutions
Romuald Lenczewski
We introduce the filtered *-bialgebra which is a noncommutative analog of the *-bialgebra of multivariate polynomials with the canonical coproduct and counit. We study the associat…
Filtered stochastic calculus
Romuald Lenczewski
By introducing a color filtration to the multiplicity space, we extend the quantum Ito calculus on multiple symmetric Fock space to the framework of filtered adapted biprocesses. I…
Limit theorems for the hierarchy of freeness
Uwe Franz, Romuald Lenczewski
The central limit theorem, the invariance principle and the Poisson limit theorem for the hierarchy of freeness are studied. We show that for given natural m the limit laws can be…
Unification of independence in quantum probability
Romuald Lenczewski
For a family of unital free *-algebras with a family of states on them, we construct a sequence of noncommutative probability spaces, which are tensor product algebras with tensor…