Free Stochastic Measures via Noncrossing Partitions

  title={Free Stochastic Measures via Noncrossing Partitions},
  author={Michael Anshelevich}
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 Itô-type relationships between free stochastic measures of different orders. These allow us to… CONTINUE READING