Lowner Evolution as Ito Diffusion

F. Bracci, M.D. Contreras, S. Diaz Madrigal [3] proved that any evaluation family of order d is described by a generalized LOwner chain. G. Ivanov and A. Vasil'ev considered randomized version of the chain and found a substitution which transforms the chain to an Ito diffusion.We generalize their result to vector randomized Lowner chain and prove there are no other possibilities to transform such Lowner chains to Ito diffusions.