Free stochastic measures via noncrossing partitions Academic Article uri icon


  • We consider free multiple stochastic measures in the combinatorial framework of the lattice of all diagonals of an n-dimensional space. In this free case, one can restrict the analysis to only the noncrossing diagonals. We give definitions of what free multiple stochastic measures are, and calculate them for the free Poisson and free compound Poisson processes. We also derive general combinatorial It-type relationships between free stochastic measures of different orders. These allow us to calculate, for example, free Poisson-Charlier polynomials, which are the orthogonal polynomials with respect to the free Poisson measure. 2000 Academic Press.

published proceedings


author list (cited authors)

  • Anshelevich, M.

citation count

  • 13

complete list of authors

  • Anshelevich, M

publication date

  • January 1, 2000 11:11 AM